Consider the problem (P) {-div(A(x, u, del u)) = lambda u^s/|x|^p + f(x) in \Omega, u(x) >= 0 in Omega, u(x) = 0 on the boundary of \Omega, where \Omega is an open bounded subset of R^N (N >= 3), 1 < p < N, \lambda and s are positive numbers, f is a nonnegative function in some Lebesgue space, A:Omega x R x RN) -> R(N) is such that c_0/(a(x) + |t |^{theta(p-1))}|\xi |^p <= < A(x, t, \xi),\ xi >, for some 0 < theta < 1, which provides a noncoercive operator when u -> infinity. The problem could be seen as a reaction model which produces a saturation effect, that is, the diffusion goes to zero when u goes to infinity. This type of reaction appears as a linearization of the Arrhenius reaction in some solid combustion problems. The aim of the article is to study existence, nonexistence and regularity of the solutions to problem (P).

Results for degenerate nonlinear elliptic equations involving a Hardy potential

MERCALDO, ANNA;
2011

Abstract

Consider the problem (P) {-div(A(x, u, del u)) = lambda u^s/|x|^p + f(x) in \Omega, u(x) >= 0 in Omega, u(x) = 0 on the boundary of \Omega, where \Omega is an open bounded subset of R^N (N >= 3), 1 < p < N, \lambda and s are positive numbers, f is a nonnegative function in some Lebesgue space, A:Omega x R x RN) -> R(N) is such that c_0/(a(x) + |t |^{theta(p-1))}|\xi |^p <= < A(x, t, \xi),\ xi >, for some 0 < theta < 1, which provides a noncoercive operator when u -> infinity. The problem could be seen as a reaction model which produces a saturation effect, that is, the diffusion goes to zero when u goes to infinity. This type of reaction appears as a linearization of the Arrhenius reaction in some solid combustion problems. The aim of the article is to study existence, nonexistence and regularity of the solutions to problem (P).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/360682
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