Existence of solutions for a cantilever beam problem

We are concerned with the fourth-order nonuniform cantilever beam problem

(I(x)WΔ∇(x)⁾Δ∇=f(x,W(x)),     

Existence of multiple solutions for a second-order difference equation with a parameter

Applying the critical point theorem, we establish existence and multiple solutions for a second-order difference boundary value problem and show the explicit intervals of λ such that the equation has at least 2N distinct solutions.     

Existence of positive solution for singular fractional differential equation

In this paper, we establish the existence of a positive solution to a singular boundary value problem of nonlinear fractional differential equation. Our analysis rely on nonlinear alternative of Leray-Schauder type and Krasnoselskii’s fixed point theorem in a cone.     

一类分数阶差分方程边值问题多重正解的存在性

考虑一类高阶分数阶差分方程边值问题.构造相关的格林函数,利用不等式技巧,分析格林函数的特征性质.运用不动点指数理论,获得了该分数阶差分方程边值问题存在多重正解的充分条件,举例说明了所获理论的有效性.     

Existence of two solutions of m-point boundary value problem for second order dynamic equations on time scales

In this paper, by means of a new twin fixed-point theorem in a cone, the existence of at least two positive solutions of m-point boundary value problem for second order dynamic equations on time scales is considered.     

Local existence of multiple positive solutions to a singular cantilever beam equation

By constructing suitable cone and control functions, we prove some local existence theorems of positive solutions for a singular fourth-order two-point boundary value problem. In mechanics, the problem is called cantilever beam equation. Furthermore, we improve a famous method appeared in the studies of singular boundary value problems. The approximation theorem of completely continuous operators and the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type play important parts in this work.     

Existence of positive solutions for singular boundary value problem on time scales

This paper deals with a class of boundary value problem of singular differential equations on time scales. The conditions we used here differ from those in the majority of papers as we know. An existence theorem of positive solutions is established by using the Krasnosel'skii fixed point theorem and an example is given to illustrate it.     

Multiple symmetric positive solutions for a second order boundary value problem

For the second order boundary value problem, , , , where growth conditions are imposed on which yield the existence of at least three symmetric positive solutions.

     

Existence of multiple positive solutions for second order nonlinear dynamic BVPs by variational methods

The aim of this paper is to employ variational techniques and critical point theory to prove some sufficient conditions for the existence of multiple positive solutions to a nonlinear second order dynamic equation with homogeneous Dirichlet boundary conditions.     

Asymptotic behavior of positive solutions for heat equation with nonlinear term

We study the nonlinear parabolic equation , in Rn×(0,∞) with boundary condition u(x,0)=u₀(x), not necessarily bounded function. The nonlinearity φ((x,t),u) is required to satisfy some conditions related to the parabolic Kato class P^∞(Rn) while allowing existence of positive solutions of the equation and continuity of such solutions. Our approach is based on potential theory tools.     

On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals

We study the existence of positive solutions for the following boundary value problem on infinite interval for second-order functional differential equations:

     

Positive solutions for boundary value problem of nonlinear fractional differential equation

In this paper, we investigate the existence and multiplicity of positive solutions for nonlinear fractional differential equation boundary value problem:

     

Existence of solutions to boundary value problems for dynamic systems on time scales

Here, we investigate systems of boundary value problems for dynamic equations on time scales. Using a generalized relationship between the boundary conditions and a certain subset of the solution space, the existence of solutions is established through topological arguments. The main tools used are Leray-Schauder and Brouwer degree theory.