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.
@article{1816,
title = {Behavior of multiple solutions for systems of semilinear elliptic equations},
journal = {CUBO, A Mathematical Journal},
year = {1995},
language = {en},
url = {http://dml.mathdoc.fr/item/1816}
}
Hernández, Gastón E. Behavior of multiple solutions for systems of semilinear elliptic equations. CUBO, A Mathematical Journal, (1995), 14 p. http://gdmltest.u-ga.fr/item/1816/