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.     

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.     

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.     

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.     

Singular mixed boundary value problem

We study singular boundary value problems with mixed boundary conditions of the form

where , , f is a nonnegative function and satisfies the Carathéodory conditions on . Here, f can have a time singularity at t=0 and/or t=T and a space singularity at x=0 and/or y=0. We present conditions for the existence of solutions positive on [0,T) and having continuous first derivatives on [0,T].     

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.     

Some multipoint boundary value problems of Neumann-Dirichlet type involving a multipoint p-Laplace like operator

Let ? and θ be two increasing homeomorphisms from R onto R with ?(0)=0, θ(0)=0. Let be a function satisfying Carathéodory's conditions, and for each i, i=1,2,…,m−2, let , be a continuous function, with , ξi∈(0,1), 0<ξ₁<ξ₂<?<ξm−2<1.In this paper we first prove a suitable continuation lemma of Leray-Schauder type which we use to obtain several existence results for the m-point boundary value problem:

     

Existence of solutions for fractional impulsive differential equations with p-Laplacian operator

We investigate the boundary value problems for nonlinear fractional impulsive differential equations with p-Laplacian operator. By applying some standard fixed point theorems, we obtain new results on the existence and uniqueness of solutions. Examples are given to show the applicability of our results.     

二阶差分方程的奇性边值问题

主要采用上下解方法,研究了一类带有奇性的二阶差分方程的两点边值问题,给出了一系列正解的存在条件.     

Uniqueness for an overdetermined boundary value problem for the p-Laplacian

For set , and let be a measure with compact support. Suppose, for , there are functions and (bounded) domains , both containing the support of with the property that in (weakly) and in the complement of . If in addition is convex, then and .

     

Three positive solutions for multipoint one-dimensional p-Laplacian boundary value problems with dependence on the first order derivative

By applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions for the one-dimensional p-Laplacian differential equation, ${\left({\varphi }_p\left(u^{\prime }\left(t\right)\right)\right)}^{\prime }+q\left(t\right)f(t,u\left(t\right),u^{\prime }\left(t\right))=0\text{,}t\in (0,1)\text{,}$ subject to the following multipoint boundary condition, $u^{\prime }\left(0\right)=\sum _{i=1}^n{\alpha }_i{u}^{\prime }\left({\xi }_i\right)\text{,}u\left(1\right)=\sum _{i=1}^n{\beta }_{i}u\left({\xi }_i\right)\text{,}$ where ${\varphi }_p\left(s\right)={\left|s\right|}^{p-2}s$ with $p>1$. The interesting point is the nonlinear term $f$ is involved with the first-order derivative explicitly.     

Uniqueness theorems for an impulsive Sturm-Liouville boundary value problem

In this study, an impulsive boundary value problem, generated by Sturm-Liouville differential equation with the eigenvalue parameter contained in one boundary condition is considered. It is shown that the coefficients of the problem are uniquely determined either by the Weyl function or by two given spectra.     

Robin boundary value problem for the Cauchy-Riemann operator

The aim of this article is to give explicit representations for solutions of the Robin boundary value problem for the Cauchy-Riemann operator [image omitted]. In the homogeneous cases we investigate the Robin boundary condition in a more general form. Finally, we give solutions of the corresponding higher-order operators.     

Positive solutions for multipoint boundary value problem of fractional differential equations

In this paper, we study the existence of positive solutions for a multi-point boundary value problem of nonlinear fractional differential equations. By applying a monotone iterative method, some existence results of positive solutions are obtained. In addition, an example is included to demonstrate the main result.     

Variational approach for a p-Laplacian boundary value problem on time scales

In this paper, we study a second-order p-Laplacian dynamic equation on a periodic time scale subject to certain boundary value conditions. The variational structure of the above-mentioned boundary value problem is presented. Some new results on the existence of at least one or three distinct periodic solutions are established by means of the saddle point theorem, the least action principle as well as the three critical point theorem.