Quasilinear Schrödinger equations involving concave and convex nonlinearities

João Marcos do Ó; Uberlandio Severo

doi:10.3934/cpaa.2009.8.621

Article Contents

2009, Volume 8, Issue 2: 621-644. Doi: 10.3934/cpaa.2009.8.621

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Quasilinear Schrödinger equations involving concave and convex nonlinearities

João Marcos do Ó^1, and
Uberlandio Severo²

1.
Departamento de Matemática, Universidade Fededral da Paraíba, 58059-900, João Pessoa-PB
2.
Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa--PB

Received: February 29, 2008

Revised: July 31, 2008

Published: February 2009

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Abstract

In this paper the mountain--pass theorem and the Ekeland variational principle in a suitable Orlicz space are employed to establish the existence of positive standing wave solutions for a quasilinear Schrödinger equation involving a combination of concave and convex terms. The second order nonlinearity considered in this paper corresponds to the superfluid equation in plasma physics.

Keywords:

Schrödinger equations,
standing wave solutions,
variational methods,
nonlinearity with concave and convex terms,
Orlicz spaces.

Mathematics Subject Classification: Primary: 35J20, 35J60; Secondary: 35Q55.

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