Multiple solutions for fourth-order boundary value problem

In this paper, we study the existence and multiplicity of nontrivial solutions for the fourth-order two point boundary value problems. Making use of the theory of fixed point index in cone and Leray-Schauder degree, under general conditions on nonlinearity, we prove that there exist at least six different nontrivial solutions for the fourth-order two point boundary value problems. Furthermore, if the nonlinearity is odd, we obtain that there exist at least eight different nontrivial solutions.     

Positive solutions of some nonlocal fourth-order boundary value problem

By the use of the Krasnosel’skii’s fixed point theorem, the existence of one or two positive solutions for the nonlocal fourth-order boundary value problem

     

Infinitely many mountain pass solutions on a kind of fourth-order Neumann boundary value problem

In this paper, the existence of infinitely many mountain pass solutions are obtained for the fourth-order boundary value problem (BVP) u⁽⁴⁾(t)-2u^″(t)+u(t)=f(u(t)),0<t<1, u^′(0)=u^′(1)=u^?(0)=u^?(1)=0, where f:R→R is continuous. The study of the problem is based on the variational methods and critical point theory. We prove the conclusion by using sub-sup solution method, Mountain Pass Theorem in Order Intervals, Leray-Schauder degree theory and Morse theory.     

Positive solutions of a second-order integral boundary value problem

In this paper we study the existence of positive solutions of a second-order integral boundary value problems for ordinary differential equations. Our results presented here unify, generalize and substantially improve the existing results in the literature. Moreover, it is worthwhile to point out that our method will dispense with constructing a new Green function.     

Existence of multiple solutions to second-order discrete Neumann boundary value problems

By using the invariant set of descending flow and variational method, we establish the existence of multiple solutions to a class of second-order discrete Neumann boundary value problems. The solutions include sign-changing solutions, positive solutions, and negative solutions. An example is given to illustrate our results.     

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。     

Three positive solutions of a nonlinear three-point boundary value problem

In this paper, existence criteria for three positive solutions of the nonlinear three-point boundary value problem

     

Blow-up analysis for solutions to Neumann boundary value problem

In this paper, we will analyze the blow-up behavior of solution sequences satisfying a conformal invariant equation defined on a compact 2-dimensional surface (M,g)$(M,g)$ with boundary. We will provide some accurate point-wise estimates for the profile of these sequences.     

Positive solutions for systems of a nonlinear fourth-order singular semipositone boundary value problems

In this paper, we study the existence of positive solutions of a two-point boundary value problem for a system of fourth-order nonlinear singular semipositone differential equations by the fixed point index theorem. Some new existence results are established, and an example is given to demonstrate the application of our main results.     

Positive solutions for a three-point boundary value problem at resonance

This paper deals with the second order three-point boundary value problem

     

Sign-changing solutions for some fourth-order nonlinear elliptic problems

In this paper, we consider the existence and multiplicity of sign-changing solutions for some fourth-order nonlinear elliptic problems and some existence and multiple are obtained. The weak solutions are sought by means of sign-changing critical theorems.     

Positive solutions of nonlinear singular third-order two-point boundary value problem

In this paper, we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem

     

Positive solutions to a multi-point higher order boundary value problem

The authors consider a higher order multi-point boundary value problem. Some existence and nonexistence results for positive solutions of the problem are obtained by using Krasnosel'skii's fixed point theorem. Examples are included to illustrate the results.     

Symmetric solutions of a multi-point boundary value problem

We apply the fixed point theorem of Avery and Peterson to the nonlinear second-order multi-point boundary value problem

     

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.     

Positive solutions of fourth-order boundary value problems with two parameters

In this paper the existence results of positive solutions are obtained for fourth-order boundary value problem

u(4)+βu″−αu=f(t,u),0<t<1,u(0)=u(1)=u″(0)=u″(1)=0,