In this note we prove the existence of radially symmetric solutions for a class of fractional Schrödinger equations in ℝN of the form (-Δ)su + V (x)u = g(u), where the nonlinearity g does not satisfy the usual Ambrosetti-Rabinowitz condition. Our approach is variational in nature, and leans on a Pohozaev identity for the fractional laplacian.
Secchi, S. (2016). On fractional schrödinger equations in ℝN without the ambrosetti-rabinowitz condition. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 47(1), 19-41 [10.12775/TMNA.2015.090].
On fractional schrödinger equations in ℝN without the ambrosetti-rabinowitz condition
SECCHI, SIMONE
Primo
2016
Abstract
In this note we prove the existence of radially symmetric solutions for a class of fractional Schrödinger equations in ℝN of the form (-Δ)su + V (x)u = g(u), where the nonlinearity g does not satisfy the usual Ambrosetti-Rabinowitz condition. Our approach is variational in nature, and leans on a Pohozaev identity for the fractional laplacian.
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