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

#### 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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