EXISTENCE AND UNIQUENESS OF BLOW-UP SOLUTIONS FOR A CLASS OF LOGISTIC EQUATIONS
Florica C. Cîrstea, Vicenţiu D. Rădulescu · Communications in Contemporary Mathematics · 2002
Let f be a non-negative C1-function on [0, ∞) such that f(u)/u is increasing and [Formula: see text], where [Formula: see text]. Assume Ω ⊂ RNis a smooth bounded domain, a is a real parameter and b ≥ 0 is a continuous function on [Formula: see text], b≢0. We consider the problem Δu+au =b(x)f(u) in Ω and we prove a necessary and sufficient condition for the existence of positive solutions that blow-up at the boundary. We also deduce several existence and uniqueness results for a related problem, subject to homogeneous Dirichlet, Neumann or Robin boundary condition.