Two nonlinear days in Urbino 2017. Electron. J. Diff. Eqns., Conference 25 (2018), pp. 149-165.

Nonhomogeneous sublinear fractional Schrodinger equations

Teresa Isernia

Abstract:
We study the existence, uniqueness and multiplicity for the sublinear fractional problem
$$ (-\Delta)^{s}u + V(x) u + a(x) |u|^{p} \text{sgn}(u) = f \quad\text{in } \mathbb{R}^N, $$
where $s\in (0, 1)$, $N>2s$, $(-\Delta)^{s}$ is the fractional Laplacian, $p\in (0, 1)$, $f\in L^2(\mathbb{R}^N) \cap L^{\frac{p+1}{p}}(\mathbb{R}^N)$, $V:\mathbb{R}^N\to \mathbb{R}$ and $a:\mathbb{R}^N\to \mathbb{R}$ are positive bounded functions.

Published September 15, 2018.
Math Subject Classifications: 35A15, 35J60, 35R11.
Key Words: Fractional Laplacian; sublinear growth; variational methods.

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Teresa Isernia
Dipartimento di Ingegneria Industriale e Scienze Matematiche
Università Politecnica delle Marche
Via Brecce Bianche, 12
60131 Ancona, Italy
email: teresa.isernia@unina.it

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