Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 579-592

MOUNTAIN PASS SOLUTIONS FOR NONLOCAL EQUATIONS

Giovanni Molica Bisci and Vicentiu D. Radulescu

Università degli Studi Mediterranea di Reggio Calabria, Dipartimento P.A.U.
Salita Melissari - Feo di Vito, 89100 Reggio Calabria, Italy; gmolica 'at' unirc.it

Institute of Mathematics "Simion Stoïlow" of the Romanian Academy
014700 Bucharest, Romania, and
University of Craiova, Department of Mathematics
200585 Craiova, Romania; vicentiu.radulescu 'at' imar.ro

Abstract. This work is devoted to study the existence of solutions to nonlocal equations involving the p-Laplacian. More precisely, we prove the existence of at least one nontrivial weak solution, and under additional assumptions, the existence of infinitely many weak solutions. In order to apply mountain pass results, we require rather general assumptions on on the local operator. Finally, a concrete application is presented.

2010 Mathematics Subject Classification: Primary 35A15, 35J20, 35J62.

Key words: p-Laplacian equations, Kirchhoff-type problems, multiple solutions, mountain pass theorem.

Reference to this article: G. Molica Bisci and V.D. Radulescu: Mountain pass solutions for nonlocal equations. Ann. Acad. Sci. Fenn. Math. 39 (2014), 579-592.

Full document as PDF file

doi:10.5186/aasfm.2014.3921