| Texto completo | |
| Autor(es): |
Harrabi, Abdellaziz
;
Hamdani, Mohamed karim
;
Fiscella, Alessio
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S; v. N/A, p. 14-pg., 2024-05-24. |
| Resumo | |
Consider the following m-polyharmonic Kirchhoff problem: M (integral(Omega) vertical bar D(r)u vertical bar(m) + a vertical bar u vertical bar(m)) [Delta(r)(m)u + a vertical bar u vertical bar m(-2)u] = K(x)f(u) in Omega, (1) where r is an element of N*, m > 1, N >= rm + 1, a >= 0 and Omega is an unbounded smooth domain. We suppose that K is an element of L-infinity(Omega) is a positive weight function, M is an element of C([0, infinity)) and f is an element of C(R) will be specified later. Using variational methods, especially the symmetric mountain pass theorem due to Rabinowitz (American Mathematical Soc., 1986), we establish the existence of infinitely many solutions of (1) where f is an odd function having quasicritical growth at infinity and satisfies a condition which is weaker than the analogue of the Ambrosetti-Rabinowitz condition. The new aspect consists in employing the Schauder basis of W-0(r,m)(Omega) (respectively of D-r,D-m(R-N)) to verify the geometry of the symmetric mountain pass theorem under a suitable condition at 0 introduced only to derive the variational setting of (1). Our results generalize and extend some existing results. (AU) | |
| Processo FAPESP: | 19/02512-5 - Sistemas e equações diferenciais parciais |
| Beneficiário: | Marcelo da Silva Montenegro |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |