Revista Matemática Iberoamericana


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Volume 32, Issue 1, 2016, pp. 1–22
DOI: 10.4171/RMI/879

Published online: 2016-02-29

Critical stationary Kirchhoff equations in $\mathbb R^N$ involving nonlocal operators

Patrizia Pucci[1] and Sara Saldi[2]

(1) Università degli Studi di Perugia, Italy
(2) Università degli Studi di Firenze, Italy

In this paper we establish existence and multiplicity of nontrivial non-negative entire (weak) solutions of a stationary Kirchhoff eigenvalue problem, involving a general nonlocal integro-differential operator. The model under consideration depends on a real parameter $\Lambda$ and involves two superlinear nonlinearities, one of which could be critical or even supercritical.

Keywords: Stationary Kirchhoff equations, existence of entire solutions, fractional Sobolev spaces, variational methods

Pucci Patrizia, Saldi Sara: Critical stationary Kirchhoff equations in $\mathbb R^N$ involving nonlocal operators. Rev. Mat. Iberoamericana 32 (2016), 1-22. doi: 10.4171/RMI/879