APPLICATION OF MOUNTAIN PASS THEOREM TO SUPERLINEAR EQUATIONS WITH FRACTIONAL LAPLACIAN CONTROLLED BY DISTRIBUTED PARAMETERS AND BOUNDARY DATA

被引：2

作者：

Bors, Dorota ^{[1
]}

机构：

[1] Univ Lodz, Fac Math & Comp Sci, Banacha 22, PL-90238 Lodz, Poland

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2018年 / 23卷 / 01期

关键词：

Boundary value problems; fractional Laplacian; stability; Mountain Pass Theorem; NONLINEAR EQUATIONS; DIFFUSION-EQUATIONS; REGULARITY;

D O I：

10.3934/dcdsb.2018003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper we consider a boundary value problem involving a differential equation with the fractional Laplacian (-Delta)(alpha/2) for alpha is an element of(1, 2) and some superlinear and subcritical nonlinearity G(z) provided with a nonhomogeneous Dirichlet exterior boundary condition. Some sufficient conditions under which the set of weak solutions to the boundary value problem is nonempty and depends continuously in the Painleve-Kuratowski sense on distributed parameters and exterior boundary data are stated. The proofs of the existence results rely on the Mountain Pass Theorem.

引用

页码：29 / 43

页数：15