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.

Iannizzotto A., Livrea R. (2021). Four Solutions for Fractional p-Laplacian Equations with Asymmetric Reactions. MEDITERRANEAN JOURNAL OF MATHEMATICS, 18(5), 1-32 [10.1007/s00009-021-01860-z].

Four Solutions for Fractional p-Laplacian Equations with Asymmetric Reactions

Livrea R.
2021

Abstract

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.
Settore MAT/05 - Analisi Matematica
https://link.springer.com/article/10.1007/s00009-021-01860-z
Iannizzotto A., Livrea R. (2021). Four Solutions for Fractional p-Laplacian Equations with Asymmetric Reactions. MEDITERRANEAN JOURNAL OF MATHEMATICS, 18(5), 1-32 [10.1007/s00009-021-01860-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/525584
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