Behavior of multiple solutions for systems of semilinear elliptic equations
Hernández, Gastón E.
In this work we present some partial results that will appear in a completed from in a forthcoming paper, . 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 ) can be established.