| Texto completo | |
| Autor(es): |
Hurtado, Elard Juarez
;
Miyagaki, Olimpio Hiroshi
;
Rodrigues, Rodrigo da Silva
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Milan Journal of Mathematics; v. 85, n. 1, p. 71-102, JUN 2017. |
| Citações Web of Science: | 2 |
| Resumo | |
In this paper, we establish existence and asymptotic behaviour of nontrivial weak solution of a class of quasilinear stationary Kirchhoff type equations involving the variable exponent spaces with critical growth, namely where is a bounded smooth domain of , with homogeneous Dirichlet boundary conditions on , the nonlinearities is a continuous function, is a function of the class , is a continuous function whose properties will be introduced later, and is a positive parameter. We assume that , where is the critical Sobolev exponent. We show that the problem has at least one solution, which it converges to zero, in the norm of the space X as . Our result extends, complement and complete in several ways some of the recent works. We want to emphasize that a difference of some previous research is that the conditions on are general enough to incorporate some differential operators of great interest. In particular, we can cover a general class of nonlocal operators for , for all . The main tools used are the Mountain Pass Theorem without the Palais-Smale condition given in {[}11] and the Concentration Compactness Principle for variable exponent found in {[}9]. We remark that it will be necessary a suitable truncation argument in the Euler- Lagrange operator associated. (AU) | |
| Processo FAPESP: | 15/11912-6 - Existência de solução para problemas elípticos |
| Beneficiário: | Rodrigo da Silva Rodrigues |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |