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March  2009, 8(2): 621-644. doi: 10.3934/cpaa.2009.8.621

Quasilinear Schrödinger equations involving concave and convex nonlinearities

João Marcos do Ó 1, and  Uberlandio Severo 2,

1. 

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

Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa--PB, Brazil

Received  March 2008 Revised  August 2008 Published  December 2008

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, Orlicz spaces, nonlinearity with concave and convex terms, standing wave solutions, variational methods.
Mathematics Subject Classification: Primary: 35J20, 35J60; Secondary: 35Q55.
Citation: João Marcos do Ó, Uberlandio Severo. Quasilinear Schrödinger equations involving concave and convex nonlinearities. Communications on Pure & Applied Analysis, 2009, 8 (2) : 621-644. doi: 10.3934/cpaa.2009.8.621
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