Work

A non-local p-Kirchhoff critical problem without the Ambrosetti-Rabinowitz condition

Year: 2024

Type: article

Abstract: In this paper, we study the existence of solutions for a non-local quasi-linear partial differential equation with a critical power in the sense of the Sobolev exponent on the right-hand side plus a subcritical perturbation. After analyzing the levels where we can recover the Cerami condition, we establish some existence results without requiring the Ambrosetti-Rabinowitz condition on the subcritical term. This paper investigates the case where the dimension N of the Euclidean space satisfies p s < N < 2 p s , and it can be seen as a continuation of some of the first author's earlier works, in which the case N > 2 p s was analyzed.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2024.129194

Author: Luigi Appolloni

Institution: University of Leeds

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,100

Funders: Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, Engineering and Physical Sciences Research Council