Abstract
AbstractThe aim of this paper is to examine the existence of at least two distinct nontrivial solutions to a Schrödinger-type problem involving the nonlocal fractional $p(\cdot )$
p
(
⋅
)
-Laplacian with concave–convex nonlinearities when, in general, the nonlinear term does not satisfy the Ambrosetti–Rabinowitz condition. The main tools for obtaining this result are the mountain pass theorem and a modified version of Ekeland’s variational principle for an energy functional with the compactness condition of the Palais–Smale type, namely the Cerami condition. Also we discuss several existence results of a sequence of infinitely many solutions to our problem. To achieve these results, we employ the fountain theorem and the dual fountain theorem as main tools.
Funder
National Research Foundation of Korea
Publisher
Springer Science and Business Media LLC
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