Abstract

CIOLETTI, L.; FERREIRA, L. C. F.  and  FURTADO, M.. An elliptic equation with random potential and supercritical nonlinearity. Integración - UIS [online]. 2019, vol.37, n.1, pp.1-16. ISSN 0120-419X.  https://doi.org/10.18273/revint.v37n1-2019001.

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.

Keywords : Elliptic equations; Random potentials; Random nonlinear equations.

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