Ground state solutions for quasilinear stationary  Schrödinger equations with critical growth

Marco A. S. Souto; Sérgio  H. M. Soares

doi:10.3934/cpaa.2013.12.99

Article Contents

2013, Volume 12, Issue 1: 99-116. Doi: 10.3934/cpaa.2013.12.99

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Ground state solutions for quasilinear stationary Schrödinger equations with critical growth

Marco A. S. Souto^1, and
Sérgio H. M. Soares^2,

1.
Universidade Federal de Campina Grande, Departamento de Matemática e Estatística, 58429-000 Campina Grande, PB
2.
Departmento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 13560-970, São Carlos, SP

Received: July 31, 2010

Revised: June 30, 2012

Published: December 2012

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Abstract

We establish the existence of ground state solution for quasilinear Schrödinger equations involving critical growth. The method used here is minimizing the gradient integral norm in a manifold defined by integrals involving the primitive of the nonlinearity function.

Keywords:

Mathematics Subject Classification: Primary: 35J20, 35J60; Secondary: 35J10.

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References

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