An elliptic equation with random potential and supercritical nonlinearity

An elliptic equation with random potential and supercritical nonlinearity

Abstract We are concerned with a nonhomogeneous elliptic equation with random potential and supercritical nonlinearity. Existence of solution is obtained almost surely for a class of potentials that includes continuum and discrete ones. Also, we provide a law of larger numbers for the obtained solut...

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Veröffentlicht in:Revista integración, temas de matematicas temas de matematicas, 2019-06, Vol.37 (1), p.1-16
Hauptverfasser: Cioletti, L., Ferreira, L. C. F., Furtado, M.
Format: Artikel
Sprache:eng
Schlagworte:
Elliptic equations
MATHEMATICS, APPLIED
Random nonlinear equations
Random potentials
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Zusammenfassung:Abstract We are concerned with a nonhomogeneous elliptic equation with random potential and supercritical nonlinearity. Existence of solution is obtained almost surely for a class of potentials that includes continuum and discrete ones. Also, we provide a law of larger numbers for the obtained solutions by independent ensembles and estimate the expected value for their L∞-norms. MSC2010: 47B80, 60H25, 35J60, 35R60, 82B44, 47H10.
ISSN:0120-419X
2145-8472
DOI:10.18273/revint.v37n1-2019001