Five solutions for the fractional $$\pmb {p}$$-Laplacian with noncoercive energy

Autor: Silvia Frassu, Antonio Iannizzotto
Rok vydání: 2022
Předmět:
Zdroj: Nonlinear Differential Equations and Applications NoDEA. 29
ISSN: 1420-9004
1021-9722
Popis: We deal with a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction which satisfies, among other hypotheses, a $$(p-1)$$ ( 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 $$(p-1)$$ ( 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.
Databáze: OpenAIRE
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