Multiple positive solutions for a class of quasi-linear elliptic equations involving concave-convex nonlinearities and Hardy terms
Center for General Education, Chang Gung University, Kwei-San, Tao-Yuan 333, Taiwan ROC
Boundary Value Problems 2011, 2011:37 doi:10.1186/1687-2770-2011-37Published: 19 October 2011
In this paper, we are concerned with the following quasilinear elliptic equation
where Ω ⊂ ℝN is a smooth domain with smooth boundary ∂Ω such that 0 ∈ Ω, Δpu = div(|∇u|p-2∇u), 1 < p < N, , λ >0, 1 < q < p, sign-changing weight functions f and g are continuous functions on , is the best Hardy constant and is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the multiplicity of positive solutions to this equation is verified.