Multiple Solutions for a Singular Quasilinear Elliptic System

الملخص EN

We consider the multiplicity of nontrivial solutions of the following quasilinear elliptic system -div(|x|-ap|∇u|p-2∇u)+f1(x)|u|p-2u=(α/(α+β))g(x)|u|α-2u|v|β+λh1(x)|u|γ-2u+l1(x), -div(|x|-ap|∇v|p-2∇v)+f2(x)|v|p-2v=(β/(α+β))g(x)|v|β-2v|u|α+μh2(x)|v|γ-2v+l2(x), u(x)>0, v(x)>0, x∈ℝN, where λ,μ>0, 10.

The functions f1(x), f2(x), g(x), h1(x), h2(x), l1(x), and l2(x) satisfy some suitable conditions.

We will prove that the problem has at least two nontrivial solutions by using Mountain Pass Theorem and Ekeland's variational principle.