Abstract
This paper is concerned with the existence of solutions to the following fractional Schrödinger type equations: -∆su+Vxu=fx,u, x∈RN, where the primitive of the nonlinearity f is of superquadratic growth near infinity in u and the potential V is allowed to be sign-changing. By using variant Fountain theorems, a sufficient condition is obtained for the existence of infinitely many nontrivial high energy solutions.
Highlights
Introduction and the Main ResultIn this work, under the assumptions that V satisfies some weaker conditions than those in [1] and the primitive of f satisfies a more general superquadratic condition near infinity, we study the existence of infinitely many nontrivial high energy solutions to the following fractional Schrodinger equations:(−)s u + V (x) u = f (x, u), x ∈ RN, (1)where s ∈ (0, 1), N > 2, and f : RN × R → R is a continuous function with some proper growth conditions
Under the assumptions that V satisfies some weaker conditions than those in [1] and the primitive of f satisfies a more general superquadratic condition near infinity, we study the existence of infinitely many nontrivial high energy solutions to the following fractional Schrodinger equations: (−)s u + V (x) u = f (x, u), x ∈ RN, (1)
Where s ∈ (0, 1), N > 2, and f : RN × R → R is a continuous function with some proper growth conditions
Summary
By using variant Fountain theorems, a sufficient condition is obtained for the existence of infinitely many nontrivial high energy solutions. x − yN+2s dy, where the symbol P.V. represents the principle value of the integral and the constant C(N, s) depends only on the space dimension N and on the order s. By Lemma 4 and conditions (f1) and (f2), we can prove that Φ is well defined and Φ ∈ C1(H) with
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