This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian:{(φ(u′))′+a(t)f(u(t))=0, 0〈t〈1, αφ(u(...This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian:{(φ(u′))′+a(t)f(u(t))=0, 0〈t〈1, αφ(u(0))-βφ(u′(ξ))=0,γφ(u(1))+δφ(u′(η))0,where φ(x) = |x|^p-2x,p 〉 1, a(t) may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple (at least three) positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.展开更多
In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we ...In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.展开更多
We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ(u′))′= λf(u), x ∈(0, 1),u′(0) = 0 = u′(1),where λ is a positive parameter, φ(s) =s/(1-s;...We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ(u′))′= λf(u), x ∈(0, 1),u′(0) = 0 = u′(1),where λ is a positive parameter, φ(s) =s/(1-s;);, f ∈ C;([0, ∞), R), f′(u) > 0 for u > 0, and for some 0 < β < θ such that f(u) < 0 for u ∈ [0, β)(semipositone) and f(u) > 0 for u > β.Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C;([0, β) ∪(β, ∞), R),f′′(u) ≥ 0 for u ∈ [0, β) and f′′(u) ≤ 0 for u ∈(β, ∞), then there exist exactly 2 n + 1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results.展开更多
In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem -△pu-∑i=1^kμi|u|^p-2/|x-ai|p^u=|u|^p^*-2u+λ|u|^q-2u,x∈Ω,where Ω belong to R^N(N ...In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem -△pu-∑i=1^kμi|u|^p-2/|x-ai|p^u=|u|^p^*-2u+λ|u|^q-2u,x∈Ω,where Ω belong to R^N(N ≥ 3) is a smooth bounded domain such that the different points ai∈Ω,i= 1,2,...,k,0≤μi〈μ^-=(N-p/p)^p,λ〉0,1≤q〈p,and p^*=p^N/N-p.The results depend crucially cn the parameters λ,q and μi for i=1,2,...,k.展开更多
In this paper, we first obtain some new results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of mu...In this paper, we first obtain some new results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.展开更多
The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples ...The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples are given to show the validity of these results.展开更多
This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t&l...This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]展开更多
In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM(εp-N∫RN|△u|p)△pu+v(x|u|p-2u=f(u)in RN, where ...In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM(εp-N∫RN|△u|p)△pu+v(x|u|p-2u=f(u)in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M : R+ → R+ and V : RN →R+ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.展开更多
In this article,we study the following critical problem involving the fractional Laplacian:{(−Δ)^α/2u−γu/|x|^α=λ|u|^q−2/|x|^s+|u|^2^∗α^(t)−2u/|x|^t in Ω,u=0 in R^N∖Ω,whereΩ⊂R^N(N>α)is a bounded smooth dom...In this article,we study the following critical problem involving the fractional Laplacian:{(−Δ)^α/2u−γu/|x|^α=λ|u|^q−2/|x|^s+|u|^2^∗α^(t)−2u/|x|^t in Ω,u=0 in R^N∖Ω,whereΩ⊂R^N(N>α)is a bounded smooth domain containing the origin,α∈(0,2),0≤s,t<α,1≤q<2,λ>0,2α^*(t)=2(N-t)/N-αis the fractional critical Sobolev-Hardy exponent,0≤γ<γH,and γH is the sharp constant of the Sobolev-Hardy inequality.We deal with the existence of multiple solutions for the above problem by means of variational methods and analytic techniques.展开更多
In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′(t) + p(t)x′(t) + q(t)x(t) = f(t, x(t)).By using Krasnoselskii fixed point...In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′(t) + p(t)x′(t) + q(t)x(t) = f(t, x(t)).By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.展开更多
In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the crit...In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the critical fractional equation.展开更多
The multiple knapsack problem (MKP) forms a base for resolving many real-life problems. This has also been considered with multiple objectives in genetic algorithms (GAs) for proving its efficiency. GAs use self- ...The multiple knapsack problem (MKP) forms a base for resolving many real-life problems. This has also been considered with multiple objectives in genetic algorithms (GAs) for proving its efficiency. GAs use self- adaptability to effectively solve complex problems with constraints, but in certain cases, self-adaptability fails by converging toward an infeasible region. This pitfall can be resolved by using different existing repairing techniques; however, this cannot assure convergence toward attaining the optimal solution. To overcome this issue, gene position-based suppression (GPS) has been modeled and embedded as a new phase in a classical GA. This phase works on the genes of a newly generated individual after the recombination phase to retain the solution vector within its feasible region and to im- prove the solution vector to attain the optimal solution. Genes holding the highest expressibility are reserved into a subset, as the best genes identified from the current individuals by re- placing the weaker genes from the subset. This subset is used by the next generated individual to improve the solution vec- tor and to retain the best genes of the individuals. Each gene's positional point and its genotype exposure for each region in an environment are used to fit the best unique genes. Further, suppression of expression in conflicting gene's relies on the requirement toward the level of exposure in the environment or in eliminating the duplicate genes from the environment.The MKP benchmark instances from the OR-library are taken for the experiment to test the new model. The outcome por- trays that GPS in a classical GA is superior in most of the cases compared to the other existing repairing techniques.展开更多
In this paper the existence and multiplicities of positive solutions for a class of quasiliear differential systems with singular nonlinearities via Leray Schauder degree theory are established.
In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of nonlinear neutral difference equation.The result is illustrated by an example.
In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of non-autonomous nonlinear neutral difference equation. We extend the results in [1].
In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u (t) + λf (t, u) = 0, t ∈ (0, 1), u (0) = sum (biu (ξ...In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u (t) + λf (t, u) = 0, t ∈ (0, 1), u (0) = sum (biu (ξ i )) from i=1 to m-2, u(1)= sum (aiu(ξ i )) from i=1 to m-2, where λ 〉 0 is a parameter, 0 〈 ξ 1 〈 ξ 2 〈 ··· 〈 ξ m 2 〈 1 with 0 〈sum ai from i=1 to m-2 〈 1, sum bi from i=1 to m-2 =1 b i 〈 1, a i , b i ∈ [0, ∞) and f (t, u) ≥ M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.展开更多
Although Successive Interference Cancellation(SIC)decoding is widely adopted in Nonorthogonal Multiple Access(NOMA)schemes for the recovery of user data at acceptable complexity,the imperfect SIC would cause Error Pro...Although Successive Interference Cancellation(SIC)decoding is widely adopted in Nonorthogonal Multiple Access(NOMA)schemes for the recovery of user data at acceptable complexity,the imperfect SIC would cause Error Propagation(EP),which can severely degrade system performance.In this work,we propose an SIC-free NOMA scheme in pulse modulation based Visible Light Communication(VLC)downlinks,including two types of users with different data rate requirements.Low bit-rate users adopt on-off keying,whereas high bit-rate ones use Multiple Pulse Position Modulation(MPPM).The soft decision decoding scheme is exploited by high bit-rate users to decode MPPM signals,which could fundamentally eliminate the detrimental effect of EP;the scheme is also easier and faster to execute compared with the conventional SIC decoding scheme.Expressions of the symbol error rate and achievable data rate for two types of users are derived.Results of the Monte Carlo simulation are provided to confirm the correctness of theoretical results.展开更多
Language testing is very important and necessary,and moreover as we all know,nowadays,in English language testing, the muhiple-choice item is most widely used and many users regard the multiple-choice item as the most...Language testing is very important and necessary,and moreover as we all know,nowadays,in English language testing, the muhiple-choice item is most widely used and many users regard the multiple-choice item as the most flexible and probably the most effective of the objective item types.The multiple-choice item has its characteristics,advantages and disadvantages.We should bring out its strengths to make up for its weaknesses and use it appropriately.Although it has its limitations,it is suitable for large-scale tests and tests dealing with wide-range knowledge.We should correctly ap- ply testing principles and methods in order to make testing more effective and reliable.展开更多
In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the...In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.展开更多
This paper presents sufficient conditions for the existence of positive solutions to some second-order system of difference equations subject to some boundary conditions. We show that it has at least three positive so...This paper presents sufficient conditions for the existence of positive solutions to some second-order system of difference equations subject to some boundary conditions. We show that it has at least three positive solutions under some assumptions by applying the fixed point theorem.展开更多
基金Tutorial Scientific Research Program Foundation of Education Department of Gansu Province(0710-04).
文摘This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian:{(φ(u′))′+a(t)f(u(t))=0, 0〈t〈1, αφ(u(0))-βφ(u′(ξ))=0,γφ(u(1))+δφ(u′(η))0,where φ(x) = |x|^p-2x,p 〉 1, a(t) may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple (at least three) positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.
文摘In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.
文摘We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ(u′))′= λf(u), x ∈(0, 1),u′(0) = 0 = u′(1),where λ is a positive parameter, φ(s) =s/(1-s;);, f ∈ C;([0, ∞), R), f′(u) > 0 for u > 0, and for some 0 < β < θ such that f(u) < 0 for u ∈ [0, β)(semipositone) and f(u) > 0 for u > β.Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C;([0, β) ∪(β, ∞), R),f′′(u) ≥ 0 for u ∈ [0, β) and f′′(u) ≤ 0 for u ∈(β, ∞), then there exist exactly 2 n + 1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results.
文摘In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem -△pu-∑i=1^kμi|u|^p-2/|x-ai|p^u=|u|^p^*-2u+λ|u|^q-2u,x∈Ω,where Ω belong to R^N(N ≥ 3) is a smooth bounded domain such that the different points ai∈Ω,i= 1,2,...,k,0≤μi〈μ^-=(N-p/p)^p,λ〉0,1≤q〈p,and p^*=p^N/N-p.The results depend crucially cn the parameters λ,q and μi for i=1,2,...,k.
基金The NSF (01BXL002) of Xuzhou Normal University and the NSF (03KJB110137) of Jingsu Education Committee.
文摘In this paper, we first obtain some new results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.
基金The Postdoctoral Science Research Foundation of Zhengzhou University.
文摘The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples are given to show the validity of these results.
基金Supported by the NSF of Guangdong Province!( 980 0 1 8) Higher Education Bureau!( 1 99873)
文摘This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]
基金supported by Natural Science Foundation of China(11371159 and 11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT_17R46
文摘In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM(εp-N∫RN|△u|p)△pu+v(x|u|p-2u=f(u)in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M : R+ → R+ and V : RN →R+ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.
文摘In this article,we study the following critical problem involving the fractional Laplacian:{(−Δ)^α/2u−γu/|x|^α=λ|u|^q−2/|x|^s+|u|^2^∗α^(t)−2u/|x|^t in Ω,u=0 in R^N∖Ω,whereΩ⊂R^N(N>α)is a bounded smooth domain containing the origin,α∈(0,2),0≤s,t<α,1≤q<2,λ>0,2α^*(t)=2(N-t)/N-αis the fractional critical Sobolev-Hardy exponent,0≤γ<γH,and γH is the sharp constant of the Sobolev-Hardy inequality.We deal with the existence of multiple solutions for the above problem by means of variational methods and analytic techniques.
基金The Science Research Plan(Jijiaokehezi[2016]166)of Jilin Province Education Department During the 13th Five-Year Periodthe Science Research Starting Foundation(2015023)of Jilin Agricultural University
文摘In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′(t) + p(t)x′(t) + q(t)x(t) = f(t, x(t)).By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.
基金supported by National Natural Science Foundation of China(11871315)Natural Science Foundation of Shanxi Province of China(201901D111021)。
文摘In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the critical fractional equation.
文摘The multiple knapsack problem (MKP) forms a base for resolving many real-life problems. This has also been considered with multiple objectives in genetic algorithms (GAs) for proving its efficiency. GAs use self- adaptability to effectively solve complex problems with constraints, but in certain cases, self-adaptability fails by converging toward an infeasible region. This pitfall can be resolved by using different existing repairing techniques; however, this cannot assure convergence toward attaining the optimal solution. To overcome this issue, gene position-based suppression (GPS) has been modeled and embedded as a new phase in a classical GA. This phase works on the genes of a newly generated individual after the recombination phase to retain the solution vector within its feasible region and to im- prove the solution vector to attain the optimal solution. Genes holding the highest expressibility are reserved into a subset, as the best genes identified from the current individuals by re- placing the weaker genes from the subset. This subset is used by the next generated individual to improve the solution vec- tor and to retain the best genes of the individuals. Each gene's positional point and its genotype exposure for each region in an environment are used to fit the best unique genes. Further, suppression of expression in conflicting gene's relies on the requirement toward the level of exposure in the environment or in eliminating the duplicate genes from the environment.The MKP benchmark instances from the OR-library are taken for the experiment to test the new model. The outcome por- trays that GPS in a classical GA is superior in most of the cases compared to the other existing repairing techniques.
文摘In this paper the existence and multiplicities of positive solutions for a class of quasiliear differential systems with singular nonlinearities via Leray Schauder degree theory are established.
文摘In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of nonlinear neutral difference equation.The result is illustrated by an example.
文摘In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of non-autonomous nonlinear neutral difference equation. We extend the results in [1].
基金Supported by Fund of National Natural Science of China (No. 10371068)Science Foundation of Business College of Shanxi University (No. 2008053)
文摘In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u (t) + λf (t, u) = 0, t ∈ (0, 1), u (0) = sum (biu (ξ i )) from i=1 to m-2, u(1)= sum (aiu(ξ i )) from i=1 to m-2, where λ 〉 0 is a parameter, 0 〈 ξ 1 〈 ξ 2 〈 ··· 〈 ξ m 2 〈 1 with 0 〈sum ai from i=1 to m-2 〈 1, sum bi from i=1 to m-2 =1 b i 〈 1, a i , b i ∈ [0, ∞) and f (t, u) ≥ M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.
基金supported by the National Key Research and Development Program of China(No.2017YFB0403403)the Natural Science Foundation of Guangdong Province(No.2015A030312006).
文摘Although Successive Interference Cancellation(SIC)decoding is widely adopted in Nonorthogonal Multiple Access(NOMA)schemes for the recovery of user data at acceptable complexity,the imperfect SIC would cause Error Propagation(EP),which can severely degrade system performance.In this work,we propose an SIC-free NOMA scheme in pulse modulation based Visible Light Communication(VLC)downlinks,including two types of users with different data rate requirements.Low bit-rate users adopt on-off keying,whereas high bit-rate ones use Multiple Pulse Position Modulation(MPPM).The soft decision decoding scheme is exploited by high bit-rate users to decode MPPM signals,which could fundamentally eliminate the detrimental effect of EP;the scheme is also easier and faster to execute compared with the conventional SIC decoding scheme.Expressions of the symbol error rate and achievable data rate for two types of users are derived.Results of the Monte Carlo simulation are provided to confirm the correctness of theoretical results.
文摘Language testing is very important and necessary,and moreover as we all know,nowadays,in English language testing, the muhiple-choice item is most widely used and many users regard the multiple-choice item as the most flexible and probably the most effective of the objective item types.The multiple-choice item has its characteristics,advantages and disadvantages.We should bring out its strengths to make up for its weaknesses and use it appropriately.Although it has its limitations,it is suitable for large-scale tests and tests dealing with wide-range knowledge.We should correctly ap- ply testing principles and methods in order to make testing more effective and reliable.
基金supported by Natural Science Foundation of Education Department of Anhui Province (KJ2008B236)
文摘In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.
基金The project was supported by the Natural Science Foundation of Hebei Province (A2006000298)the Doctoral Program Foundation of Hebei Province (B2004204).
文摘This paper presents sufficient conditions for the existence of positive solutions to some second-order system of difference equations subject to some boundary conditions. We show that it has at least three positive solutions under some assumptions by applying the fixed point theorem.