Infinitely many solutions for a critical Kirchhoff type problem\n involving a fractional operator

2015/05/16 by Alessio Fiscella, Fiscella, Alessio
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1505.04280

openalex publication_date 2015/05/16 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28

Abstract

In this paper we deal with a Kirchhoff type problem driven by a fractional\nnonlocal integrodifferential operator - mathcal L_K and involving a critical\nnonlinearity. For this problem we prove the existence of infinitely many\nsolutions, through a suitable truncation argument and exploiting the genus\ntheory introduced by Krasnoselskii.\n

Related

• Stationary Kirchhoff problems involving a fractional elliptic operator\n and a critical nonlinearity
• On Critical Kirchhoff problems driven by the fractional Laplacian
• Existence and Multiplicity of Nontrivial Weak Solutions for Kirchhoff-type Fractional p-Laplacian Equation
• Fractional Kirchhoff problem with critical indefinite nonlinearity
• Signed and sign-changing solutions for a class Kirchhoff-type problem involving the fractional p-Laplacian with critical Hardy nonlinearity