Existence results for fractional p-Laplacian problems via Morse theory

By Antonio Iannizzotto, Shibo Liu, Kanishka Perera, Marco Squassina. 2014

264 citations recorded by the source corpus.

Abstract We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear problems involving the fractional Laplacian and arising in the framework of continuum mechanics, phase transition phenomena, population dynamics and game theory. Under different growth assumptions on the reaction term, we obtain various existence as well as finite multiplicity results by means of variational and topological methods and, in particular, arguments from Morse theory.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/1e7a6567dcb94048bc6ea6a268cf0bb2bcf9b7aa

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Optimal decay of extremals for the fractional Sobolev inequality (2015, background): “See also [11,17,18,20] and the references therein for some existence and regularity results.”
Bifurcation and multiplicity results for critical fractional p‐Laplacian problems (2014, methodology): “e standard scheme based on the genus does not give the index information necessary for our purposes here, so we will use the following scheme based on the cohomological index as in Iannizzotto et al. [27] (see also Perera [32]). Let Ψ(u) = 1 |u|p p , u ∈ M = u ∈ Xs p(Ω) : kuk = 1 . Then eigenvalues ”
Global H\"older regularity for the fractional $p$-Laplacian (2014, methodology): “While undoubtedly being relevant in light of the applications depicted in [10], we do not treat this problem here.”
Multiplicity results for the non-homogeneous fractional p-Kirchhoff equations with concave–convex nonlinearities (2015, background): “for x ∈Rn, see [1–4] and the references therein for further details on the fractional p-Laplacian.”
Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p-Laplacian in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setl (2015, background): “for x ∈ RN , where Bε(x) := {y ∈ RN : |x − y| < ε}, see [26–28,32] and the references therein for further details on the fractional p-Laplacian.”
A Hopf's lemma and a strong minimum principle for the fractional p-Laplacian (2016, background): “See for instance [10, 5, 6, 12, 21, 23, 24, 31, 19] and the references therein.”
Critical Nonlocal Systems with Concave-Convex Powers (2016, background): “Some results about the existence of solutions have been considered in [13, 18, 21], see also the references therein.”