Minimal potential results for Schrodinger equations with Neumann boundary conditions

被引：1

作者：

Edward, Julian ^{[1
]}

Hudson, Steve ^{[1
]}

Leckband, Mark ^{[1
]}

机构：

[1] Florida Int Univ, Dept Math & Stat, Miami, FL 33199 USA

来源：

FORUM MATHEMATICUM | 2017年 / 29卷 / 06期

关键词：

Minimal potential results; Schrodinger equation; p-Laplacian; MEAN-VALUE ZERO; OPERATORS; INEQUALITY; LAPLACIAN; BALL;

D O I：

10.1515/forum-2015-0082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the boundary value problem -Delta(p)u = V vertical bar u vertical bar(p-2) u - C, where u is an element of W-1,W- p (D) is assumed to satisfy Neumann boundary conditions, and D is a bounded domain in R-n. We derive necessary conditions for the existence of nontrivial solutions. These conditions usually involve a lower bound for the product of a sharp Sobolev constant and an L-p norm of V. When p = n, Orlicz norms are used. In many cases, these inequalities are best possible. Applications to linear and non-linear eigenvalue problems are also discussed.

引用

页码：1337 / 1348

页数：12

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