Revista Matemática Iberoamericana
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Published online: 2016-02-29
Critical stationary Kirchhoff equations in $\mathbb R^N$ involving nonlocal operatorsPatrizia Pucci and Sara Saldi (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. Iberoam. 32 (2016), 1-22. doi: 10.4171/RMI/879