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Indexed by:期刊论文

Date of Publication:2019-01-01

Journal:COMMUNICATIONS ON PURE AND APPLIED ANALYSIS

Included Journals:SCIE

Volume:18

Issue:1

Page Number:51-64

ISSN No.:1534-0392

Key Words:Quasilinear Schrodinger equation; positive solution; asymptotically cubic; Nehari manifold

Abstract:We consider the following quasilinear Schrodinger equation
   -Delta u + V(x)u - Delta(u(2))u = q(x)g(u), x is an element of R-N,R-
   where N >= 1, 0 < q(x) <= lim(vertical bar x vertical bar ->infinity) q(x), g is an element of C (R+, R) and g(u)/u(3)-> 1, as u ->infinity. We establish the existence of a positive solution to this problem by using the method developed in Szulkin and Weth [27, 28].