6533b7d5fe1ef96bd1263c8a

RESEARCH PRODUCT

Four solutions for fractional p-Laplacian equations with asymmetric reactions

Antonio IannizzottoRoberto Livrea

subject

Sublinear functionGeneral MathematicsMathematical analysisDegenerate energy levelsType (model theory)Fractional p-LaplacianCritical point (mathematics)Dirichlet distributionNonlinear systemsymbols.namesakeMathematics - Analysis of PDEsSettore MAT/05 - Analisi Matematicacritical point theory35A15 35R11 58E05p-LaplaciansymbolsFOS: Mathematicsasymmetric reactionsMathematicsMorse theoryAnalysis of PDEs (math.AP)

description

We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, whose reaction combines a sublinear term depending on a positive parameter and an asymmetric perturbation (superlinear at positive infinity, at most linear at negative infinity). By means of critical point theory and Morse theory, we prove that, for small enough values of the parameter, such problem admits at least four nontrivial solutions: two positive, one negative, and one nodal. As a tool, we prove a Brezis-Oswald type comparison result.

yearjournalcountryeditionlanguage
2020-10-25
http://arxiv.org/abs/2010.13151