INVESTIGADORES
TOSCHI Marisa
artículos
Título:
On the existence of bounded solutions for a nonlinear elliptic system
Autor/es:
DURÁN, RICARDO; SANMARTINO, MARCELA; TOSCHI, MARISA
Revista:
ANNALI DI MATEMATICA PURA ED APPLICATA
Editorial:
SPRINGER HEIDELBERG
Referencias:
Año: 2012 vol. 191 p. 771 - 782
ISSN:
0373-3114
Resumen:
This work deals with the system $(-Delta)^m u= a(x), v^p$, $(-Delta)^m v=b(x), u^q$ with Dirichlet boundary condition in a domain $OmegasubsetRR^n$, where $Omega$ is a ball if $nge 3$ or a smooth perturbation of a ball when $n=2$. We prove that, under appropriate conditions on the parameters ($a,b,p,q,m,n$), any non-negative solution $(u,v)$ of the system is bounded by a constant independent of $(u,v)$. Moreover, we prove that the conditions are sharp in the sense that, up to some border case, the relation on the parameters are also necessary. The case $m=1$ was considered by Souplet in cite{PS}. Our paper generalize to $mge 1$ the results of that paper.