Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Existence of Multi-peak Solutions for a Class of Quasilinear Problems in Orlicz-Sobolev Spaces

Existence of Multi-peak Solutions for a Class of Quasilinear Problems in Orlicz-Sobolev Spaces The aim of this work is to establish the existence of multi-peak solutions for the following class of quasilinear problems − div ( ϵ 2 ϕ ( ϵ | ∇ u | ) ∇ u ) + V ( x ) ϕ ( | u | ) u = f ( u ) in  R N , $$ - \mbox{div} \bigl(\epsilon^{2}\phi\bigl(\epsilon|\nabla u|\bigr)\nabla u \bigr) + V(x)\phi\bigl(\vert u\vert\bigr)u = f(u)\quad\mbox{in } \mathbb{R}^{N}, $$ where ϵ $\epsilon$ is a positive parameter, N ≥ 2 $N\geq2$ , V $V$ , f $f$ are continuous functions satisfying some technical conditions and ϕ $\phi$ is a C 1 $C^{1}$ -function. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Existence of Multi-peak Solutions for a Class of Quasilinear Problems in Orlicz-Sobolev Spaces

Loading next page...
 
/lp/springer-journals/existence-of-multi-peak-solutions-for-a-class-of-quasilinear-problems-V03KtQZKO6

References (44)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-017-0107-4
Publisher site
See Article on Publisher Site

Abstract

The aim of this work is to establish the existence of multi-peak solutions for the following class of quasilinear problems − div ( ϵ 2 ϕ ( ϵ | ∇ u | ) ∇ u ) + V ( x ) ϕ ( | u | ) u = f ( u ) in  R N , $$ - \mbox{div} \bigl(\epsilon^{2}\phi\bigl(\epsilon|\nabla u|\bigr)\nabla u \bigr) + V(x)\phi\bigl(\vert u\vert\bigr)u = f(u)\quad\mbox{in } \mathbb{R}^{N}, $$ where ϵ $\epsilon$ is a positive parameter, N ≥ 2 $N\geq2$ , V $V$ , f $f$ are continuous functions satisfying some technical conditions and ϕ $\phi$ is a C 1 $C^{1}$ -function.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Jun 14, 2017

There are no references for this article.