Large solutions for non-divergence structure equations with singular lower order terms

Abstract

In this paper we investigate infinite boundary value problems associated with the semi-linear PDE Lu=k(x)f(u) on a bounded smooth domain Ω⊂Rn, where L is a non-divergence structure, uniformly elliptic operator with singular lower order terms. The weight k is a continuous non-negative function and f is a continuous nondecreasing function that satisfies the Keller–Osserman condition. We study a sufficient condition on k that ensures existence of a large solution u. In case the lower order terms of L are bounded, under further assumptions on f and k we establish asymptotic bounds of solutions u near the boundary ∂Ω and, as a consequence a uniqueness result.