| Texto completo | |
| Autor(es): |
Ghosh, Sekhar
;
Choudhuri, Debajyoti
;
Fiscella, Alessio
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | FRACTIONAL CALCULUS AND APPLIED ANALYSIS; v. 28, n. 2, p. 28-pg., 2025-02-26. |
| Resumo | |
We study the existence of nonnegative solutions to the following nonlocal elliptic problem involving singularity M(integral(Q)|u(x)-u(y)|(p) / |x-y|(N+ps) dxdy)(-Delta)(p)(s)u=lambda/u(gamma)+u(ps & lowast;)-1 in Omega, u>0 in Omega, u=0 in R-N\Omega, where M is the Kirchhoff function, Q=R-2N\((R-N\Omega)x(R-N\Omega)), Omega subset of R-N, is a bounded domain with Lipschitz boundary, lambda>0, N>ps, 0<s,gamma<1, (-Delta)(p)(s) is the fractional p-Laplacian for 1<p<infinity and p(s)(& lowast;)=Np/N-ps is the critical Sobolev exponent. We employ a cut-off argument to obtain the existence of k (being arbitrarily large integer) solutions. Furthermore, by using the Moser iteration technique, we prove an uniform L-infinity(Omega) bound for the solutions. The novelty of this work lies in proving the existence of small energy solutions by using symmetric mountain pass theorem in spite of the presence of a critical nonlinear term which, of course, is super-linear. (AU) | |
| Processo FAPESP: | 24/04156-0 - Problemas não uniformemente elípticos |
| Beneficiário: | Alessio Fiscella |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |