Existence of symmetric positive solutions for a boundary value problem with integral boundary conditions

This paper studies the existence of symmetric positive solutions for a second-order nonlinear ordinary differential equation with integral boundary conditions by applying the theory of fixed point index in cones. For the demonstration of the results, an illustrative example is presented.     

Remarks on nonlocal boundary value problems at resonance

We show that it is important to allow the nonlinear term to change sign when discussing existence of a positive solution for multipoint, or more general nonlocal, boundary value problems in the resonant case. When the nonlinear term has a fixed sign we obtain simple necessary and sufficient conditions for the existence of positive solutions.     

Existence of symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems

This paper deals with the existence of symmetric positive solutions for a class of singular Sturm-Liouville-like boundary value problems with a one-dimensional p-Laplacian operator. By using the fixed theorem of cone expansion and compression of norm type in a cone, the existence of positive solutions is established though nonlinear term contains the first derivative of unknown function.     

含积分边界条件的分数阶微分方程边值问题的正解的存在性

研究了含积分边界条件的分数阶微分方程的边值问题,首先给出格林函数及性质,其次将问题转化为一个等价的积分方程,最后应用Krasnoselkii及Leggett-Williams不动点定理得到了一个及多个正解的存在性,推广了以往的结果．     

一般Lidstone边值问题的n个正解的存在性

考察了含所有偶数阶导数的一般Lidstone边值问题的正解和对称正解.通过 选择合适的Banach空间和锥,对该问题建立了n个正解或者对称正解的存在性,其 中n是一个任意的自然数.基本工具是等价范数和锥拉伸与锥压缩型的Krasnosel'skii 不动点定理. 结论的主要条件是局部的.换言之,如果非线性项f在某些有界集上的 "高度"是适当的,则该问题可以具有n个正解.     

一类二阶离散Neumann边值问题正解的存在性

研究一类二阶离散Neumann边值问题正解的存在性,运用不动点指数理论获得了方程存在正解的最优条件,并给出一个具体例子说明这一结果。     

Positive solutions of discrete third-order three-point right focal boundary value problems

We consider linear and nonlinear boundary value problems for third-order difference equations with three-point right focal boundary conditions. In the linear case, the existence of positive solutions corresponding to the first eigenvalue of the problem is established and an interval estimate for the first eigenvalue is obtained. In the nonlinear case, sufficient conditions for the existence and nonexistence of positive solutions are obtained. An example is included at the end of the paper to illustrate the sharpness of our results.     

二阶三点边值问题正解的存在性

利用不动点指数定理研究了一类二阶非线性常微分方程的三点边值问题正解的存在性问题,得到了至少存在一个或无穷多个正解的几个充分条件.     

Nonsymmetric solutions of a nonlinear boundary value problem

We study the existence and multiplicity of positive nonsymmetric and signchanging nonantisymmetric solutions of a nonlinear second order ordinary differential equation with symmetric nonlinear boundary conditions, where both of the nonlinearities are of power type. The given problem has already been studied by other authors, but the number of its positive nonsymmetric and sign-changing nonantisymmetric solutions has been determined only under some technical conditions. It was a long-standing open question whether or not these conditions can be omitted. In this article we provide the answer. Our main tool is the shooting method.     

Positive solutions of higher-order nonlinear fractional differential systems with nonlocal boundary conditions

The paper deals with the existence and multiplicity of positive solutions for a system of higher-order nonlinear fractional differential equations with nonlocal boundary conditions. The main tool used in the proof is fixed point index theory in cone. Some limit type conditions for ensuring the existence of positive solutions are given.     

Positive solutions for an n-point nonhomogeneous boundary value problem

This paper is concerned with the solvability of an n-point nonhomogeneous boundary value problem. By using the Krasnoselskii's fixed-point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of at least one positive solution are established for the n-point nonhomogeneous boundary value problem.     

一类四阶差分方程多点边值问题的正解

为解决多点支撑弹性梁的正解的存在性问题,运用锥上不动点指数理论,研究一类含参四阶差分方程多点边值问题.获得了当参数在一定范围内取值时正解的存在性结果,得到了正解存在的充分条件.     

Multiple positive solutions for discrete nonlocal boundary value problems

In this paper, we investigate a second-order nonlinear difference equation with sign-changing nonlinearity subject to two different sets of nonlocal boundary conditions. The explicit expressions of the associated Green's functions are presented. By using a recently developed fixed point theorem, we establish sufficient conditions for the existence of multiple positive solutions of the boundary value problem.     

Positive solutions of a general discrete boundary value problem

In this paper, the existence of positive solutions for a nonlinear general discrete boundary value problem is established. Such results extend and improve some known facts for the two-point and three-point boundary value problems. Particularly, the boundary value conditions can be nonlinear and the method is new. For explaining the main results, some numerical examples are also given.     

Initial boundary value problems for quasilinear symmetric hyperbolic systems with characteristic boundary

This paper is devoted to initial boundary value problems for quasi-linear symmetric hyperbolic systems in a domain with characteristic boundary. It extends the theory on linear symmetric hyperbolic systems established by Friedrichs to the nonlinear case. The concept on regular characteristics and dissipative boundary conditions are given for quasilinear hyperbolic systems. Under some assumptions, an existence theorem for such initial boundary value problems is obtained. The theorem can also be applied to the Euler system of compressible flow. __________ Translated from Chinese Annals of Mathematics, Ser. A, 1982, 3(2): 223–232     

Blow-up and global solutions for quasilinear parabolic equations with Neumann boundary conditions

Using the upper and lower solution techniques and Hopf's maximum principle, the sufficient conditions for the existence of blow-up positive solution and global positive solution are obtained for a class of quasilinear parabolic equations subject to Neumann boundary conditions. An upper bound for the ‘blow-up time’, an upper estimate of the ‘blow-up rate’, and an upper estimate of the global solution are also specified.     

Necessary conditions for the existence of positive solutions to fractional boundary value problems at resonance

In this article, we obtain some properties of the positive solutions to a class of fractional differential equation multipoint boundary value problems at resonance. Necessary conditions for the existence of positive solutions are established by means of the spectral theory of linear operator. As application, necessary and sufficient conditions for the existence of positive solutions are given for the case that the nonlinearity has a fixed sign. Some examples are presented to illustrate our results.     

Positive solutions of a nonlinear impulsive equation with periodic boundary conditions

In this paper, we investigate nonlinear second order differential equations subject to linear impulse conditions and periodic boundary conditions. Sign properties of an associated Green’s function are exploited to get existence results for positive solutions of the nonlinear boundary value problem with impulse. Upper and lower bounds for positive solutions are also given. The results obtained yield periodic positive solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis.     

Existence of positive solutions to n-point nonhomogeneous boundary value problem

In this paper, we are concerned with the existence of positive solutions to a n-point nonhomogeneous boundary value problem. By using the Krasnoselskii's fixed point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of positive solution is established for the n-point nonhomogeneous boundary value problem.     

Positive solutions for a class of fractional differential equations with integral boundary conditions

The existence of positive solutions for a class of fractional equations involving the Riemann–Liouville fractional derivative with integral boundary conditions is investigated. By means of the monotone iteration method and some inequalities associated with the Green function, we obtain the existence of a positive solution and establish the iterative sequence for approximating the solution.