Multiple Positive Solutions for a Quasilinear Elliptic System Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

Abstract EN

Let Ω∋0 be an-open bounded domain in RN(N≥3) and p*=(pN/(N-p)).

We consider the following quasilinear elliptic system of two equations in W01,p(Ω)×W01,p(Ω): -Δpu=λf(x)|u|q-2u+(α/(α+β))h(x)|u|α-2u|v|β,-Δpv=μg(x)|v|q-2v+(β/(α+β))h(x)|u|α|v|β -2v, where λ, μ>0, Δp denotes the p-Laplacian operator, 1≤q1 satisfy p<α+β≤p*, and f, g, h are continuous functions on Ω¯ which are somewhere positive but which may change sign on Ω.

We establish the existence and multiplicity results of positive solutions to (the above mentioned quasilinear elliptic system equations) by variational methods.