In this paper we present some new existence results for singular boundary value problems by Arzela-Ascoli theorem. In particular our nonlinearity may be singular in its dependent variable.
By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive soluti...By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.展开更多
The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0...The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.展开更多
The authors study the existence of positive solutions to the boundary value problem where f and e: [r,R] x [0,∞) → R are two continuous functions satisfying f 0 and |e| M for some M > 0. The authors show that...The authors study the existence of positive solutions to the boundary value problem where f and e: [r,R] x [0,∞) → R are two continuous functions satisfying f 0 and |e| M for some M > 0. The authors show that there exists at least one positive solution in the following two cases: (i) f is superlinear at infinity and λ > 0 is small enough; (ii) f is sublinear at infinity and λ > 0 is large enough. Their proofs are based on fixed point theorems in cones.展开更多
In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower soluti...In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.展开更多
Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear 4n-th-order differential equationy (4n)=f(t,y,y′,y″,...,y (4n-1))(a)with the boundary conditions g 2i(y (2i)(a),y (2i+1...Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear 4n-th-order differential equationy (4n)=f(t,y,y′,y″,...,y (4n-1))(a)with the boundary conditions g 2i(y (2i)(a),y (2i+1)(a))=0,h 2i(y (2i)(c),y (2i+1)(c))=0,(i=0,1,...,2n-1)(b) where the functions f, g i and h i are continuous with certain monotone properties. For the boundary value problems of nonlinear nth order differential equationy (n)=f(t,y,y′,y″,...,y (n-1))many results have been given at the present time. But the existence of solutions of boundary value problem (a),(b) studied in this paper has not been covered by the above researches. Moreover, the corollary of the important theorem in this paper, i.e. existence of solutions of the boundary value problem.y (4n)=f(t,y,y′,y″,...,y (4n-1)) a 2iy (2i)(a)+a 2i+1y (2i+1)(a)=b 2i,c 2iy (2i)(c)+c 2i+1y (2i+1)(c)=d 2i,(i=0,1,...2n-1)has not been dealt with in previous works.展开更多
In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by vi...We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder＇s inequality, a suitable singular Cronwall＇s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.展开更多
In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(...In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.展开更多
By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existen...By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.展开更多
This paper deals with the existence of positive solutions of the equation u'+f(t, u)=0 with linear boundary conditions. We show the existence of at least one positive solution if / is neither superlinear nor subli...This paper deals with the existence of positive solutions of the equation u'+f(t, u)=0 with linear boundary conditions. We show the existence of at least one positive solution if / is neither superlinear nor sublinear on u by a simple application of a fixed point Theorem in cones.展开更多
In this paper, we investigate the solvability of boundary value problems for a class of vibration differential equation describing the fractional order damped system with signal stimulus. By presenting kernel function...In this paper, we investigate the solvability of boundary value problems for a class of vibration differential equation describing the fractional order damped system with signal stimulus. By presenting kernel function through the Laplace transform, and using the eigenvalue and the improved Leray-Schauder degree, the existence of solutions for boundary value problems is established.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
1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1...1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1（Rn）→LQ（RN）. Kurtz has discussed the existence of κ-node solution of （1.1）, （1.2） for each κ∈N U{0} when the growth rate of |u|l-1u+f（u） is lower then |u|v+3/v-1 i.e.展开更多
TFD ( Thomas-Fermi-Dirac) equation in quantum mechanics is established. The existence theorems of the solutions are obtained by singular boundary value problem theory of ordinary differential equation and upper and lo...TFD ( Thomas-Fermi-Dirac) equation in quantum mechanics is established. The existence theorems of the solutions are obtained by singular boundary value problem theory of ordinary differential equation and upper and lower solution method.展开更多
In this paper, we establish the existence of positive solutions of (|y'| p-2g' )'+f(t,y)= 0 (P>1 ). y (0)=y (1) = 0. The function f is allowed to be singular when y= 0.
In this paper, by use of the Schauder fixed-point theorem, the existence of solution of （k, n - k） Conjugate boundary value problems in Banach spaces is investigated.
By using the method of upper and lower solution, some conditions of the existence of solutions of nonlinear two-point boundary value problems for 4nth-order nonlinear differential equation are studied.
In this paper,a multi-point boundary value problems for a three order nonlinear deferential equation is considered.With the help of coincidence theorem due to Mawhin,a existence theorem is obtained.
文摘In this paper we present some new existence results for singular boundary value problems by Arzela-Ascoli theorem. In particular our nonlinearity may be singular in its dependent variable.
文摘By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.
文摘The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.
基金Supported by Natural Science Foundation of ChinaFoundation of Key Teacher of University of Education Ministry
文摘The authors study the existence of positive solutions to the boundary value problem where f and e: [r,R] x [0,∞) → R are two continuous functions satisfying f 0 and |e| M for some M > 0. The authors show that there exists at least one positive solution in the following two cases: (i) f is superlinear at infinity and λ > 0 is small enough; (ii) f is sublinear at infinity and λ > 0 is large enough. Their proofs are based on fixed point theorems in cones.
文摘In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.
文摘Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear 4n-th-order differential equationy (4n)=f(t,y,y′,y″,...,y (4n-1))(a)with the boundary conditions g 2i(y (2i)(a),y (2i+1)(a))=0,h 2i(y (2i)(c),y (2i+1)(c))=0,(i=0,1,...,2n-1)(b) where the functions f, g i and h i are continuous with certain monotone properties. For the boundary value problems of nonlinear nth order differential equationy (n)=f(t,y,y′,y″,...,y (n-1))many results have been given at the present time. But the existence of solutions of boundary value problem (a),(b) studied in this paper has not been covered by the above researches. Moreover, the corollary of the important theorem in this paper, i.e. existence of solutions of the boundary value problem.y (4n)=f(t,y,y′,y″,...,y (4n-1)) a 2iy (2i)(a)+a 2i+1y (2i+1)(a)=b 2i,c 2iy (2i)(c)+c 2i+1y (2i+1)(c)=d 2i,(i=0,1,...2n-1)has not been dealt with in previous works.
文摘In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
基金supported by Grant In Aid research fund of Virginia Military Instittue, USA
文摘We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder＇s inequality, a suitable singular Cronwall＇s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.
基金Supported by the Foundation of the Office of Science and Technology of Henan(122102310373)Supported by the NSF of Education Department of Henan Province(12B110025)
文摘In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.
基金supported by Scientific Research Fund of Heilongjiang Provincial Education Department (11544032)the National Natural Science Foundation of China (10571021, 10701020)
文摘By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.
文摘This paper deals with the existence of positive solutions of the equation u'+f(t, u)=0 with linear boundary conditions. We show the existence of at least one positive solution if / is neither superlinear nor sublinear on u by a simple application of a fixed point Theorem in cones.
文摘In this paper, we investigate the solvability of boundary value problems for a class of vibration differential equation describing the fractional order damped system with signal stimulus. By presenting kernel function through the Laplace transform, and using the eigenvalue and the improved Leray-Schauder degree, the existence of solutions for boundary value problems is established.
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.
文摘1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1（Rn）→LQ（RN）. Kurtz has discussed the existence of κ-node solution of （1.1）, （1.2） for each κ∈N U{0} when the growth rate of |u|l-1u+f（u） is lower then |u|v+3/v-1 i.e.
文摘TFD ( Thomas-Fermi-Dirac) equation in quantum mechanics is established. The existence theorems of the solutions are obtained by singular boundary value problem theory of ordinary differential equation and upper and lower solution method.
文摘In this paper, we establish the existence of positive solutions of (|y'| p-2g' )'+f(t,y)= 0 (P>1 ). y (0)=y (1) = 0. The function f is allowed to be singular when y= 0.
文摘In this paper, by use of the Schauder fixed-point theorem, the existence of solution of （k, n - k） Conjugate boundary value problems in Banach spaces is investigated.
文摘By using the method of upper and lower solution, some conditions of the existence of solutions of nonlinear two-point boundary value problems for 4nth-order nonlinear differential equation are studied.
基金Supported by Nature Science Foundation of Education Department of Henan Province（2010A110023）
文摘In this paper,a multi-point boundary value problems for a three order nonlinear deferential equation is considered.With the help of coincidence theorem due to Mawhin,a existence theorem is obtained.
