Existence of semiclassical states for a quasilinear Schrödinger equation on .N with exponential critical growth

Authors
Li, Shao Jun Santos, Carlos A. Yang, Min Bo
Citation
Li, Shao Jun et al., Existence of semiclassical states for a quasilinear Schrödinger equation on .N with exponential critical growth, Acta mathematica Sinica. English series (Print) , 32(11), 2016, pp. 1279-1296
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
32
Issue
11
Year of publication
2016
Pages
1279 - 1296
Database
ACNP
SICI code
Abstract
We study a quasilinear Schrödinger equation {..N.Nu+V(x)|u|N.2u=Q(x)f(u)inRN,0<u.W1,N(RN),u(x).....|x|..0, where V,Q are two continuous real functions on .N and . > 0 is a real parameter. Assume that the nonlinearity f is of exponential critical growth in the sense of Trudinger.Moser inequality, we are able to establish the existence and concentration of the semiclassical solutions by variational methods.