A concave—convex elliptic problem involving the fractional Laplacian

A concave—convex elliptic problem involving the fractional Laplacian

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 a...

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Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2013-02, Vol.143 (1), p.39-71
Hauptverfasser: Brändle, C., Colorado, E., de Pablo, A., Sánchez, U.
Format: Artikel
Sprache:eng
Schlagworte:
Inequalities
Mathematics
Nonlinearity
Operators
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Zusammenfassung: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.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210511000175