Release Time:2019-03-13  Hits:

Indexed by: Journal Article

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: 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].