A concave—convex elliptic problem involving the fractional Laplacian

C. Brändle; E. Colorado; A. de Pablo; U. Sánchez

doi:10.1017/S0308210511000175

Abstract

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We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave—convex term. We completely characterize the range of parameters for which solutions of the problem exist and prove a multiplicity result. We also prove an associated trace inequality and some Liouville-type results.

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A concave—convex elliptic problem involving the fractional Laplacian

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