This paper deals with the existence of infinitely many solutions for a class of Dirichlet elliptic problems driven by a bi-nonlocal operator u → M(∥u∥2)(-Δ)su, where M models a Kirchhoff-type coefficient while (-Δ)s denotes the fractional Laplace operator. More precisely, by adapting to our bi-nonlocal framework the variational and topological tools introduced in [16], we establish the existence of infinitely many solutions. The main feature and difficulty of our problems is due to the possible degenerate nature of the Kirchhoff term M.
D'Onofrio, L., Fiscella, A., Molica Bisci, G. (2017). Perturbation methods for nonlocal Kirchhoff-type problems. FRACTIONAL CALCULUS & APPLIED ANALYSIS, 20(4), 829-853 [10.1515/fca-2017-0044].
Perturbation methods for nonlocal Kirchhoff-type problems
Fiscella A;
2017
Abstract
This paper deals with the existence of infinitely many solutions for a class of Dirichlet elliptic problems driven by a bi-nonlocal operator u → M(∥u∥2)(-Δ)su, where M models a Kirchhoff-type coefficient while (-Δ)s denotes the fractional Laplace operator. More precisely, by adapting to our bi-nonlocal framework the variational and topological tools introduced in [16], we establish the existence of infinitely many solutions. The main feature and difficulty of our problems is due to the possible degenerate nature of the Kirchhoff term M.
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