| Texto completo | |
| Autor(es): |
Figueiredo, Giovany M.
;
Pimenta, Marcos T. O.
;
Winkert, Patrick
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 251, p. 14-pg., 2024-10-01. |
| Resumo | |
In this paper we study the asymptotic behavior of solutions to the (p,q)-equation -Delta(p)u-Delta(q)u=f(x,u )in Omega, u=0 on partial derivative Omega, as p -> 1+, where N >= 2, & colone;1<p<q<1 & lowast;& colone;N/(N-1) and f is a Carath & eacute;odory function that grows superlinearly and subcritically. Based on a Nehari manifold treatment, we are able to prove that the (1,q)-Laplace problem given by -div(del u|del u|)-Delta(q)u=f(x,u) in Omega, u=0 on partial derivative Omega, has at least two constant sign solutions and one sign-changing solution, whereby the sign-changing solution has least energy among all sign-changing solutions. Furthermore, the solutions belong to the usual Sobolev space W-0(1,q)(Omega) which is in contrast with the case of 1-Laplacian problems, where the solutions just belong to the space BV(Omega) of all functions of bounded variation. As far as we know this is the first work dealing with (1,q)-Laplace problems even in the direction of constant sign solutions. (AU) | |
| Processo FAPESP: | 21/04158-4 - Problemas elípticos envolvendo o operador de curvatura-média no espaço das funções de variação limitada |
| Beneficiário: | Marcos Tadeu de Oliveira Pimenta |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 23/06617-1 - EDPs elípticas quasilineares envolvendo o operador (1,q)-laplaciano e o operador double phase |
| Beneficiário: | Marcos Tadeu de Oliveira Pimenta |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 23/10287-7 - Existência de soluções positivas e nodais para equações elípticas locais e não-locais |
| Beneficiário: | Marcos Tadeu de Oliveira Pimenta |
| Modalidade de apoio: | Auxílio à Pesquisa - Pesquisador Visitante - Brasil |