Release Time:2019-03-11  Hits:

Indexed by: Journal Article

Date of Publication: 2017-11-01

Journal: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS

Included Journals: SCIE、Scopus

Volume: 16

Issue: 6

Page Number: 2105-2123

ISSN: 1534-0392

Key Words: Penalization techniques; Ljusternik-Schnirelmann theory; fractional Schrodinger equation; multiple solutions; single spike solutions

Abstract: Using penalization techniques and the Ljusternik-Schnirelmann theory, we establish the multiplicity and concentration of solutions for the following fractional Schrodinger equation
   { epsilon(2 alpha) (-Delta)(alpha)u + V(x)u = f(u), x is an element of R-N, u is an element of H-alpha (R-N), u > 0, x is an element of R-N,
   where 0 < alpha < 1, N > 2 alpha, epsilon > 0 is a small parameter, V satisfies the local condition, and f is superlinear and subcritical nonlinearity. We show that this equation has at least cat M-delta (M) single spike solutions.