Existence of Solutions for a Variable Exponent System without PS Conditions

Li Yin, Yuan Liang, Qihu Zhang, Chunshan Zhao

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we study the existence of solution for the following elliptic system of variable exponents with perturbation terms ∇div jrujp(x)∇2ru) + jujp(x)∇2u = γ a(x)juj(x)∇2u + Fu(x; u; v) in RN; ∇div jrvjq(x)∇2rv) + jvjq(x)∇2v = γ b(x)jvjγ (x)∇2v + Fv(x; u; v) in RN; u 2 W1;p(γ)(RN); v 2 W1;q(γ)(RN); where the corresponding functional does not satisfy PS conditions. We obtain a suγ cient condition for the existence of solution and also present a result on asymptotic behavior of solutions at inγ nity. where the corresponding functional does not satisfy PS conditions. We obtain a suffcient condition for the existence of solution and also present a result on asymptotic behavior of solutions at inffnity.

Original languageAmerican English
JournalElectronic Journal of Differential Equations
Volume2015
StatePublished - Mar 1 2015

Keywords

  • Integral functional
  • PS condition
  • Variable exponent Sobolev space
  • Variable exponent system

DC Disciplines

  • Education
  • Mathematics

Fingerprint

Dive into the research topics of 'Existence of Solutions for a Variable Exponent System without PS Conditions'. Together they form a unique fingerprint.

Cite this