This paper shows the existence of nontrivial weak solutions for the quasilinear elliptic equation
in . Here is a positive continuous potential bounded away from zero and is a nonlinear term of subcritical type. Using minimax methods, we show the existence of a nontrivial solution in and then show that it decays to zero at infinity when .
Submitted October 27, 2007. Published April 17, 2008.
Math Subject Classifications: 35J20, 35J60, 35Q55.
Key Words: Quasilinear Schrodinger equation; solitary waves; p-Laplacian; variational method; mountain-pass theorem.
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| Uberlandio Severo |
Departamento de Matemática, Universidade Federal da Paraí ba
58051-900, João Pessoa, PB , Brazil
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