General uniqueness results for large solutions

Abstract

We give a series of very general sufficient conditions in order to ensure the uniqueness of large solutions for --$\Delta$u + f (x, u) = 0 in a bounded domain $\Omega$ where f : $\Omega$ x R $\rightarrow$ R + is a continuous function, such that f (x, 0) = 0 for x $\in$ $\Omega$, and f (x, r) > 0 for x in a neighborhood of $\partial$$\Omega$ and all r > 0. 2010 Mathematics Subject Classification. 35 J 61; 31 B 15; 28 C 05 .