Four solutions for fractional p-Laplacian equations with asymmetric\n reactions

2020/10/25 by Roberto Livrea, Livrea, Roberto, Antonio Iannizzotto +1
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2010.13151

Abstract

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

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