Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2015-04-10

Journal: ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

Included Journals: SCIE

ISSN: 1072-6691

Key Words: Quasilinear Schrodinger equation; local linking; fountain theorem; indefinite potential

Abstract: In this article, we study the existence and multiplicity of solutions of the quasilinear Schrodinger equation
   -u '' + V(x)u - ( broken vertical bar u broken vertical bar(2))'' u = f (u)
   on R, where the potential V allows sign changing and the nonlinearity satisfies conditions weaker than the classical Ambrosetti-Rabinowitz condition. By a local linking theorem and the fountain theorem, we obtain the existence and multiplicity of solutions for the equation.