Infinitely many solutions for fractional Schrödinger equation with potential vanishing at infinity

Abstract

The paper investigates the following fractional Schrödinger equation: (-) s u + V(x)u = K(x)f (u), x ∈ R N , where 0 < s < 1, 2s < N, (-) s is the fractional Laplacian operator of order s. V(x), K(x) are nonnegative continuous functions and f (x) is a continuous function satisfying some conditions. The existence of infinitely many solutions for the above equation is presented by using a variant fountain theorem, which improves the related conclusions on this topic. The interesting result of this paper is the potential V(x) vanishing at infinity, i.e., lim |x|→+∞ V(x) = 0.

Existence and Symmetry of Solutions for a Class of Fractional Schrödinger–Poisson Systems

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Existence and multiplicity of solutions for fractional Schödinger equation involving a critical nonlinearity

“…Recently, the fractional Schödinger equation has became a fundamental equation in fractional quantum mechanics, where, when ε → 0 is taken in (1.2), the existence of solutions is very important; see [14] and the references therein. In the past few years, many works were devoted to establishing the existence and multiplicity of solutions of fractional Schödinger equation, see [15][16][17][18][19][20][21][22] and the references therein. Recently, the existence of solutions of fractional Schödinger equation with perturbation was investigated, see [18][19][20][21].…”

Existence of solutions for asymptotically periodic fractional Schrödinger equation with critical growth

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