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Behavior of multiple solutions for systems of semilinear elliptic equations

Author
Hernández, Gastón E.

Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/1816
Abstract
In this work we present some partial results that will appear in a completed from in a forthcoming paper, [7]. We discuss the existence and particularly the multiplicity of solutions for the nonlinear system of elliptic equations. Δui + λfi (x, u1, . . . um) = 0    in    Ω      (1.1) uiǀ𝜃Ω = 0,    i = 1 , . . . , m                     (1.2) Where fi (x, 0, . . . 0) > 0 for all x ⋲ Ω,  i = 1, 2, . . . , m. The functions fi,  i = 1, . . . , m, satisfy the quasimonotone condition and a certain blow up rate us to be made precise in the assumptions (H1) and (H2) below. Then results similar to those of the scalar equation case (see [6]) can be established.   
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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
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Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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