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

Abstract

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