Existence and multiplicity results for the fractional Schrödinger equations with indefinite potentials. Issue 6 (26th April 2021) - Cui, Na; Sun, Hong-Rui
ABSTRACT: In this paper, we consider the fractional Schrödinger equations ( − Δ ) s u + V ( x ) u = f ( x, u ) in   R N, where s ∈ (0, 1) and N >2 s . Firstly, we prove that the problem admits a nontrivial solution and infinitely many nontrivial solutions under the assumptions that V is allowed to be indefinite potential and f is superlinear and subcritical. In addition, we establish an existence criterion of infinitely many nontrivial solutions for the aforementioned problem with concave and critical nonlinearities as well as indefinite potential, which improves the result of Du and Tian [Infinitely many solutions of the nonlinear fractional Schrödinger equations. Discrete Contin Dyn Syst B. 2016;21(10):3407–3428 (Theorem 1.6)].