Existence and uniqueness of large solutions for a class of non-uniformly elliptic semilinear equations

Abstract

In this paper, we study existence, uniqueness, and asymptotic behavior of large solutions of second-order degenerate elliptic semilinear problems in non-divergence form. The main particularity of the problem is the interior uniform ellipticity of the equation, which degenerates on the boundary, involving an effect on the boundary blow-up profile of the solution.