We deal with a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction which satisfies, among other hypotheses, a (p- 1) -linear growth at infinity with non-resonance above the first eigenvalue. The energy functional governing the problem is thus noncoercive. We focus on the behavior of the reaction near the origin, assuming that it has a (p- 1) -sublinear growth at zero, vanishes at three points, and satisfies a reverse Ambrosetti–Rabinowitz condition. Under such assumptions, by means of critical point theory and Morse theory, and using suitably truncated reactions, we show the existence of five nontrivial solutions: two positive, two negative, and one nodal.

Five solutions for the fractional p -Laplacian with noncoercive energy

Frassu S.
;
Iannizzotto A.
2022-01-01

Abstract

We deal with a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction which satisfies, among other hypotheses, a (p- 1) -linear growth at infinity with non-resonance above the first eigenvalue. The energy functional governing the problem is thus noncoercive. We focus on the behavior of the reaction near the origin, assuming that it has a (p- 1) -sublinear growth at zero, vanishes at three points, and satisfies a reverse Ambrosetti–Rabinowitz condition. Under such assumptions, by means of critical point theory and Morse theory, and using suitably truncated reactions, we show the existence of five nontrivial solutions: two positive, two negative, and one nodal.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/342376
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