Nonnegative Entire Bounded Solutions to some Semilinear Equations Involving the Fractional Laplacian

Nonnegative Entire Bounded Solutions to some Semilinear Equations Involving the Fractional Laplacian

We establish necessary and sufficient conditions under which the fractional semilinear elliptic equation Δ α 2 u = ρ ( x ) φ ( u ) admits nonnegative nontrivial bounded solutions in the whole space ℝ N .

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Veröffentlicht in:Potential analysis 2018-05, Vol.48 (4), p.495-513
Hauptverfasser: Chrouda, Mohamed Ben, Fredj, Mahmoud Ben
Format: Artikel
Sprache:eng
Schlagworte:
Functional Analysis
Geometry
Mathematics
Mathematics and Statistics
Potential Theory
Probability Theory and Stochastic Processes
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Zusammenfassung:We establish necessary and sufficient conditions under which the fractional semilinear elliptic equation Δ α 2 u = ρ ( x ) φ ( u ) admits nonnegative nontrivial bounded solutions in the whole space ℝ N .
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-017-9645-7