Ground state solutions of asymptotically linear fractional Schrödinger equations

Abstract

Orbital and asymptotic stability for standing waves of a nonlinear Schrödinger equation with concentrated nonlinearity in dimension three This paper is devoted to a time-independent fractional Schrödinger equation of the formwhere N ≥ 2, s ∈ (0, 1), ( − ) s stands for the fractional Laplacian. We apply the variational methods to obtain the existence of ground state solutions when f(x, u) is asymptotically linear with respect to u at infinity. C 2013 AIP Publishing LLC. [http://dx.

Ground state solutions of scalar field fractional Schrödinger equations

“…Moreover, fractional Schrödinger-type problems have been considered in some interesting papers [2,17,18]. In addition, nonlocal fractional equations appear in many fields and a lot of interest has been devoted to this kind of problems and to their concrete applications; see, for instance the seminal papers [12][13][14] and [3,9,15,22,40,57], as well as the references therein.…”

Energy solutions and concentration problem of fractional Schrödinger equation

“…By using a new function space introduced in [38,39] and constructing some inequalities, we can obtain the concentration of the solutions of (1.1) under different conditions. Hence our results can be viewed as an extension to the main results in [16][17][18][19][20][21][22][23]38]. We list the following assumptions.…”

“…In [17], Chang obtained the existence and multiplicity of solutions when the nonlinear term f satisfies the asymptotically linear case and under the condition:…”

Nontrivial Solution for the Fractional p-Laplacian Equations via Perturbation Methods

“…For the proof of the lemma, it was proved in [27] in the case = 2. For the general case, the proof is similar.…”