A Critical Concave–Convex Kirchhoff-Type Equation in $$\mathbb R^4$$ Involving Potentials Which May Vanish at Infinity

Autor:	Marcelo C. Ferreira, Pedro Ubilla
Rok vydání:	2021
Předmět:	Nuclear and High Energy Physics Dimension (graph theory) Mathematical analysis Vanish at infinity Mathematics::Analysis of PDEs Regular polygon Statistical and Nonlinear Physics Sobolev space Nonlinear system Compact space Compactness theorem Critical exponent Mathematical Physics Mathematics
Zdroj:	Annales Henri Poincaré. 23:25-47
ISSN:	1424-0661 1424-0637
DOI:	10.1007/s00023-021-01105-5
Popis:	We establish the existence and multiplicity of solutions for a Kirchhoff-type problem in $$\mathbb R^4$$ involving a critical and concave–convex nonlinearity. Since in dimension four, the Sobolev critical exponent is $$2^*=4$$ , there is a tie between the growth of the nonlocal term and the critical nonlinearity. This turns out to be a challenge to study our problem from the variational point of view. Some of the main tools used in this paper are the mountain-pass and Ekeland’s theorems, Lions’ Concentration Compactness Principle and an extension to $$\mathbb R^N$$ of the Struwe’s global compactness theorem.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ecdd07b0dafe3affa6d88c3f9aeaf220 https://doi.org/10.1007/s00023-021-01105-5 Zobrazit plný text záznamu Full text from SpringerLink