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Multiple solutions for a semilinear nonhomogeneous 1 elliptic system | Abstract
Mathematica Eterna

Mathematica Eterna
Open Access

ISSN: 1314-3344

+12 184512974

Abstract

Multiple solutions for a semilinear nonhomogeneous 1 elliptic system

Xiaodong Zhao and Lin Chen

In this paper, by the Mountain Pass Theory and Ekeland’s variational principle, we consider the existence and multiplicity of nontrivial solutions for the nonhomogeneous semilinear elliptic system ? ?? ?? −???u + u = α α+β f(x)|u| α−2u|v| β + l1(x), x ∈ ???, −???v + v = β α+β f(x)|u| α|v| β−2v + l2(x), x ∈ ???, ∂u ∂n = λg(x)|u| q−2u, ∂v ∂n = µh(x)|v| q−2 v, x ∈ ∂???, where ??? is a bounded domain in R N with smooth boundary, α > 1, β > 1 satisfying 2 < α+β < 2 ∗ (2∗ = 2N N−2 if N ≥ 3, 2 ∗ = ∞ if N = 2), 1 < q < 2, the pair of parameters (λ, µ) ∈ R 2 \ {(0, 0)}

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