Two nonlinear days in Urbino 2017. Electron. J. Diff. Eqns., Conference 25 (2018), pp. 221-233.

Ground state solutions for Bessel fractional equations with irregular nonlinearities

Simone Secchi

Abstract:
We consider the semilinear fractional equation
$$ (I-\Delta)^s u = a(x) |u|^{p-2}u \quad\text{in }\mathbb{R}^N, $$
where $N \geq 3$, 0<s<1, 2<p<2N/(N-2s) and a is a bounded weight function. Without assuming that a has an asymptotic profile at infinity, we prove the existence of a ground state solution.

Published September 15, 2018.
Math Subject Classifications: 35KJ60, 35Q55, 35S05.
Key Words: Bessel fractional operator, fractional Laplacian.

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Simone Secchi
Dipartimento di Matematica e Applicazioni
Università degli Studi di Milano Bicocca
email: simone.secchi@unimib.it

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