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Abstract

This paper is concerned with a class of fractional Schrödinger equation with Hardy potential $\begin{array}{l} {(- Δ)}^{s} u + V (x) u - \frac{κ}{| x |^{2 s}} u = f (x, u), x \in R^{N}, \end{array}$ where $s \in (0, 1)$ and $κ ⩾ 0$ is a parameter. Under some suitable conditions on the potential V and the nonlinearity f, we prove the existence of ground state solutions when the parameter κ lies in a given range by using the non-Nehari manifold method. Moreover, we investigate the continuous dependence of ground state energy about κ. Finally, we are able to explore the asymptotic behavior of ground state solutions when κ tends to 0.

Keywords

Fractional Schrödinger equation Hardy potential Strongly indefinite functional Ground state solutions

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On nonlinear fractional Schrödinger equations with indefinite and Hardy potentials

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