We study the asymptotic behavior, as γ tends to infinity, of solutions for the homogeneous Dirichlet problem associated with singular semilinear elliptic equations whose model is -Δu=f(x)uγinΩ,where Ω is an open, bounded subset of RN and f is a bounded function. We deal with the existence of a limit equation under two different assumptions on f: either strictly positive on every compactly contained subset of Ω or only nonnegative. Through this study, we deduce optimal existence results of positive solutions for the homogeneous Dirichlet problem associated with -Δv+|∇v|2v=finΩ.

Asymptotic behavior and existence of solutions for singular elliptic equations / Durastanti, R.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 199:3(2020), pp. 925-954. [10.1007/s10231-019-00906-0]

Asymptotic behavior and existence of solutions for singular elliptic equations

Durastanti R.
2020

Abstract

We study the asymptotic behavior, as γ tends to infinity, of solutions for the homogeneous Dirichlet problem associated with singular semilinear elliptic equations whose model is -Δu=f(x)uγinΩ,where Ω is an open, bounded subset of RN and f is a bounded function. We deal with the existence of a limit equation under two different assumptions on f: either strictly positive on every compactly contained subset of Ω or only nonnegative. Through this study, we deduce optimal existence results of positive solutions for the homogeneous Dirichlet problem associated with -Δv+|∇v|2v=finΩ.
Asymptotic behavior; Quasilinear elliptic equations; Semilinear elliptic equations; Singular elliptic equations; Singular natural growth gradient terms
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Asymptotic behavior and existence of solutions for singular elliptic equations / Durastanti, R.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 199:3(2020), pp. 925-954. [10.1007/s10231-019-00906-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1415218
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