TITLE

# Solitary waves for a class of quasilinear SchrÃ¶dinger equations in dimension two

AUTHOR(S)
do Ó, João Marcos; Severo, Uberlandio
PUB. DATE
July 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Jul2010, Vol. 38 Issue 3/4, p275
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
In this paper we prove the existence and concentration behavior of positive ground state solutions for quasilinear SchrÃ¶dinger equations of the form âˆ’ Îµ2Î” u + V( z) u âˆ’ Îµ2 [Î”( u2)] u = h( u) in the whole two-dimension space where Îµ is a small positive parameter and V is a continuous potential uniformly positive. The main feature of this paper is that the nonlinear term h( u) is allowed to enjoy the critical exponential growth with respect to the Trudingerâ€“Moser inequality and also the presence of the second order nonhomogeneous term [Î”( u2)] u which prevents us to work in a classical Sobolev space. Using a version of the Trudingerâ€“Moser inequality, a penalization technique and mountain-pass arguments in a nonstandard Orlicz space we establish the existence of solutions that concentrate near a local minimum of V.
ACCESSION #
50354930

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