The existence of solutions for a second-order discrete Neumann problem with a p-Laplacian

In this paper, we investigate the solutions of second-order discrete Neumann boundary value problem with a p-Laplacian. By using critical point theory the existence results are obtained.     

Existence of solutions for discrete p-Laplacian with potential boundary conditions

We are concerned with the existence of solutions for some discrete p-Laplacian equations subjected to a potential type boundary condition. Our approach is a variational one and relies on Szulkin's critical point theory. We obtain the existence of solutions in a coercive case as well as the existence of non-trivial solutions when the corresponding energy functional has a ‘mountain pass’ geometry.     

Three solutions for a p-Laplacian boundary value problem with impulsive effects

In this paper, a p-Laplacian boundary value problem with impulsive effects is considered. Multiplicity of solutions is obtained by three critical points theorem. An example is presented to illustrate main result.     

Positive solutions for a fractional boundary value problem with p-Laplacian operator

In this paper, we are mainly concerned with positive solutions for a p-Laplacian fractional boundary value problem. By virtue of Jensen’s inequalities and some new properties of the Green function of the problem, we adopt the Krasnoselskii-Zabreiko fixed point theorem to establish the results of existence and multiplicity of the positive solutions. Finally, a uniqueness theorem is established by using a fixed point theorem of concave operator and an example is given to illustrate the result.     

Existence of solutions for a nonlinear discrete system involving the p-Laplacian

The existence of solutions for boundary value problems for a nonlinear discrete system involving the p-Laplacian is investigated. The approach is based on critical point theory.     

非对称p-Laplacian Dirichlet问题的非平凡解

研究了一类非对称的p-Laplacian(p1)Dirichlet问题.在正半轴不需要假设Ambrosetti-Rabinowitz的超二次条件下,利用山路定理建立非平凡解的存在性结果.     

Infinitely many solutions for a p-Laplacian boundary value problem with impulsive effects

In this paper, a p-Laplacian boundary value problem with impulsive effects is considered. By using variational methods and critical point theorems, some criteria are obtained to guarantee that the impulsive problem has infinitely many solutions when the impulsive functions satisfy superlinear or sublinear conditions. Our results further improve some existing results.     

Periodic and subharmonic solutions of discrete p-Laplacian systems

Some solvability conditions of periodic and subharmonic solutions are obtained for a class of discrete p-Laplacian systems by the minimax methods in critical point theory.     

Existence of weak solutions for impulsive p-Laplacian problem with superlinear impulses

Using the critical point theory we are going to prove the existence of one and then of many weak solutions under subtle conditions for impulsive $p$-Laplacian problem. The novice lies in the fact that we do not restrict ourselves to sublinear impulses. We also prove existence of at least one non-positive and one non-negative solution, when $p=2$.     

Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian

This paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93-104].     

Positive solutions for a p-Laplacian type system of impulsive fractional boundary value problem

In this paper, the aim is to discuss a class of p-Laplacian type fractional Dirichlet"s boundary value problem involving impulsive impacts. Based on the approaches of variational method and the properties of fractional derivatives on the reflexive Banach spaces, the existence results of positive solutions for our equations are established. Two examples are given at the end of each main result.     

具p-Laplace算子的分数阶微分方程边值问题的正解

考虑具有p-Laplace算子的分数阶泛函微分方程边值问题,利用锥上的不动点定理,得到了其正解及多个正解存在的充分条件,所得结果推广了已有的结论,并举例说明了结论的适用性.     

Signed and sign-changing solutions for a Kirchhoff-type problem involving the fractional p-Laplacian with critical Hardy nonlinearity

In this paper, we study the existence of three solutions for a Kirchhoff equation involving the nonlocal fractional p-Laplacian considering Sobolev and Hardy nonlinearities at subcritical and critical growths. The proof is based on mountain pass theorem and constrained minimization in Nehari sets.     

Positive solutions for a second-order three-point discrete boundary value problem

We establish the existence of at least three positive solutions for the second-order three-point discrete boundary value problem: $$\Delta ^{2}y(k-1)+f(k,y(k))=0,\quad k\in \{1,\ldots ,T\},$$ $$y(0)=0,\quad y(T+1)=\alpha y(n),$$ where f is continuous, T≥3 and n∈{2,…,T?1} are two fixed positive integers, constant α>0 such that α n<T+1. Under suitable conditions, we accomplish this by using the property of the associate Green’s function and Leggett-Williams fixed point theorem.     

带p-Laplacian算子的分数阶微分方程非局部边值问题解的存在性

利用经典的Schaefer不动点定理,研究了一类带有p-Laplacian算子的非线性分数阶微分方程非局部边值问题,在适当的假设条件下,得到了解的存在性结果.并举例说明结果的应用.