On the existence of bounded solutions for a nonlinear elliptic system

This work deals with the system (-Δ) mu = a(x) v p, (-Δ) mv = b(x) u q with Dirichlet boundary condition in a domain Ω ⊂ ℝ n, where Ω is a ball if n ≥ 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 nonnegative so...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Durán, R.G., Sanmartino, M., Toschi, M.
Formato: JOUR
Materias:
A priori estimates
Critical exponents
Elliptic systems
Weighted Sobolev spaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03733114_v191_n4_p771_Duran
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_03733114_v191_n4_p771_Duran
record_format dspace
spelling todo:paper_03733114_v191_n4_p771_Duran2023-10-03T15:30:18Z On the existence of bounded solutions for a nonlinear elliptic system Durán, R.G. Sanmartino, M. Toschi, M. A priori estimates Critical exponents Elliptic systems Weighted Sobolev spaces This work deals with the system (-Δ) mu = a(x) v p, (-Δ) mv = b(x) u q with Dirichlet boundary condition in a domain Ω ⊂ ℝ n, where Ω is a ball if n ≥ 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 nonnegative 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 (Nonlinear Partial Differ Equ Appl 20:464-479, 2004). Our paper generalize to m ≥ 1 the results of that paper. © 2011 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03733114_v191_n4_p771_Duran
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic A priori estimates
Critical exponents
Elliptic systems
Weighted Sobolev spaces
spellingShingle A priori estimates
Critical exponents
Elliptic systems
Weighted Sobolev spaces
Durán, R.G.
Sanmartino, M.
Toschi, M.
On the existence of bounded solutions for a nonlinear elliptic system
topic_facet A priori estimates
Critical exponents
Elliptic systems
Weighted Sobolev spaces
description This work deals with the system (-Δ) mu = a(x) v p, (-Δ) mv = b(x) u q with Dirichlet boundary condition in a domain Ω ⊂ ℝ n, where Ω is a ball if n ≥ 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 nonnegative 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 (Nonlinear Partial Differ Equ Appl 20:464-479, 2004). Our paper generalize to m ≥ 1 the results of that paper. © 2011 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
format JOUR
author Durán, R.G.
Sanmartino, M.
Toschi, M.
author_facet Durán, R.G.
Sanmartino, M.
Toschi, M.
author_sort Durán, R.G.
title On the existence of bounded solutions for a nonlinear elliptic system
title_short On the existence of bounded solutions for a nonlinear elliptic system
title_full On the existence of bounded solutions for a nonlinear elliptic system
title_fullStr On the existence of bounded solutions for a nonlinear elliptic system
title_full_unstemmed On the existence of bounded solutions for a nonlinear elliptic system
title_sort on the existence of bounded solutions for a nonlinear elliptic system
url http://hdl.handle.net/20.500.12110/paper_03733114_v191_n4_p771_Duran
work_keys_str_mv AT duranrg ontheexistenceofboundedsolutionsforanonlinearellipticsystem
AT sanmartinom ontheexistenceofboundedsolutionsforanonlinearellipticsystem
AT toschim ontheexistenceofboundedsolutionsforanonlinearellipticsystem
_version_ 1807320066705850368

Ejemplares similares