In this paper we consider the following problem: −div(A(x, u)∇u) = u^s + f(x) in Ω, u(x) \ge 0 in Ω, u(x) = 0 on ∂Ω, where Ω is an open bounded subset of R^N, N\ge 3, and A : Ω × R → M_N×N is an elliptic matrix such that when u→∞ is non-coercive, s is a nonnegative number less then 1. We prove existence results for weak solutions and for renormalized solutions to non-homogeneous or homogeneous problem.
Existence results for semilinear elliptic equations with some lack of coercivity / Mercaldo, Anna; I., Peral. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - STAMPA. - 138:3(2008), pp. 569-595. [10.1017/S0308210506000126]
Existence results for semilinear elliptic equations with some lack of coercivity
MERCALDO, ANNA;
2008
Abstract
In this paper we consider the following problem: −div(A(x, u)∇u) = u^s + f(x) in Ω, u(x) \ge 0 in Ω, u(x) = 0 on ∂Ω, where Ω is an open bounded subset of R^N, N\ge 3, and A : Ω × R → M_N×N is an elliptic matrix such that when u→∞ is non-coercive, s is a nonnegative number less then 1. We prove existence results for weak solutions and for renormalized solutions to non-homogeneous or homogeneous problem.| File | Dimensione | Formato | |
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