A discontinuous problem involving the p-Laplacian operator and critical exponent in ℝN

Abstract

Using convex analysis, we establish the existence of at least two nonnegative solutions for the quasilinear problem -Δpu = H(u - α)u p*-1 + λh(x) in ℝN where Δpu is the p-Laplacian operator, H is the Heaviside function, p* is the Sobolev critical exponent, and h is a positive function.