This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global min...We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.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
In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam wh...In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.展开更多
By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam w...By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.展开更多
This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems ...This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.展开更多
Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of ...Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.展开更多
In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term witho...In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.展开更多
The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″(t) + q(t)f(t,u(t),u′(t)) = 0, 0 〈 t 〈 1, u(0) = u″(0) = u′(1) = 0 is studied....The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″(t) + q(t)f(t,u(t),u′(t)) = 0, 0 〈 t 〈 1, u(0) = u″(0) = u′(1) = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.展开更多
An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, ...An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.展开更多
The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and se...The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and several existence theorems of positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist.展开更多
The existence of positive solutions and the global attractivity of the difference equation Δy n=r ny nK-y n-l n K-cy n-l n are investigated. And some sufficient conditions are obtained,which greatly imp...The existence of positive solutions and the global attractivity of the difference equation Δy n=r ny nK-y n-l n K-cy n-l n are investigated. And some sufficient conditions are obtained,which greatly improve and extend the known results.展开更多
In this paper, using fixed theorem in cones, the authors obtain the existence of multiple positive solutions on the following boundary value problem u"+a(t)f(u)=0,t∈[0,1],u(0)=0,au(η)^*=u(1).
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
A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the crite...A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the criteria existing in literature. Our conditions are necessary and suffcient when all the coeffcients of the equations are constants.展开更多
The existence of positive radial solutions to the systems of m(m≥1) semilinear elliptic equations Δu+p(r)f(u)=0,0<A<r<B in annuli with Dirichlet(Dirichlet/Neumann)boundary conditions,is studied,whe...The existence of positive radial solutions to the systems of m(m≥1) semilinear elliptic equations Δu+p(r)f(u)=0,0<A<r<B in annuli with Dirichlet(Dirichlet/Neumann)boundary conditions,is studied,where r=x 2 1+...+x 2 n,n≥1.u=(u 1,...,u m),p(r)f(u)=(p 1(r)f 1(u),...,p m(r)f m(u)), and p(r) may be singular at r=A or r=B,f may be singular at u=0.展开更多
In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K(x)is a positive function in L^s(R^N) for some s 〉 1and th...In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K(x)is a positive function in L^s(R^N) for some s 〉 1and the nonnegative functions f, g ∈ C(R, R) are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N.展开更多
In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Alle...In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. We also prove some nonexistence results.展开更多
This paper investigates the boundary value problem for elastic beam equation of the formu″″(t) q(t)f(t, u(t),u′(t),u″(t),u′″(t)), 0〈t〈1,with the boundary conditionsu=(0)=u′(1)=u″(0)=u′″...This paper investigates the boundary value problem for elastic beam equation of the formu″″(t) q(t)f(t, u(t),u′(t),u″(t),u′″(t)), 0〈t〈1,with the boundary conditionsu=(0)=u′(1)=u″(0)=u′″(1)=0.The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternate, Leray-Schauder fixed point theorem and a fixed point theorem due to Avery and Peterson, we establish some results on the existence and multiplicity of positive solutions to the boundary value problem. Our results extend and improve some recent work in the literature.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.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.
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.
文摘In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.
文摘By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.
基金The research supported by the National Natural Science Foundation of China.
文摘This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.
文摘Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.
基金supported by Science and Technology Project of Chongqing Municipal Education Committee (kJ110501) of ChinaNatural Science Foundation Project of CQ CSTC (cstc2012jjA20016) of ChinaNational Natural Science Foundation of China (11101298)
文摘In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.
基金Supported by the Natural Science Foundation of Zhejiang Province (Y605144)the XNF of Zhejiang University of Media and Communications (XN080012008034)
文摘The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″(t) + q(t)f(t,u(t),u′(t)) = 0, 0 〈 t 〈 1, u(0) = u″(0) = u′(1) = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.
文摘An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.
文摘The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and several existence theorems of positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist.
文摘The existence of positive solutions and the global attractivity of the difference equation Δy n=r ny nK-y n-l n K-cy n-l n are investigated. And some sufficient conditions are obtained,which greatly improve and extend the known results.
基金the Natural Science Foundation of China(10271095)
文摘In this paper, using fixed theorem in cones, the authors obtain the existence of multiple positive solutions on the following boundary value problem u"+a(t)f(u)=0,t∈[0,1],u(0)=0,au(η)^*=u(1).
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A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the criteria existing in literature. Our conditions are necessary and suffcient when all the coeffcients of the equations are constants.
基金The work was supported by NNSF(1 9771 0 0 7) of China
文摘The existence of positive radial solutions to the systems of m(m≥1) semilinear elliptic equations Δu+p(r)f(u)=0,0<A<r<B in annuli with Dirichlet(Dirichlet/Neumann)boundary conditions,is studied,where r=x 2 1+...+x 2 n,n≥1.u=(u 1,...,u m),p(r)f(u)=(p 1(r)f 1(u),...,p m(r)f m(u)), and p(r) may be singular at r=A or r=B,f may be singular at u=0.
基金supported by NSFC(11071095)Hubei Key Laboratory of Mathematical Sciences
文摘In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K(x)is a positive function in L^s(R^N) for some s 〉 1and the nonnegative functions f, g ∈ C(R, R) are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N.
基金supported by the National Natural Science Foundation of China (No.10671049)the US-NSF grants (No.DMS-0314736)
文摘In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. We also prove some nonexistence results.
基金supported by the Natural Science Foundation of Zhejiang Province of China (Y605144)
文摘This paper investigates the boundary value problem for elastic beam equation of the formu″″(t) q(t)f(t, u(t),u′(t),u″(t),u′″(t)), 0〈t〈1,with the boundary conditionsu=(0)=u′(1)=u″(0)=u′″(1)=0.The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternate, Leray-Schauder fixed point theorem and a fixed point theorem due to Avery and Peterson, we establish some results on the existence and multiplicity of positive solutions to the boundary value problem. Our results extend and improve some recent work in the literature.
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.