A semilinear singular Sturm–Liouville equation involving measure data

Abstract

Given α>0 and p>1, let μ be a bounded Radon measure on the interval (−1,1). We are interested in the equation −(|x|2αu′)′+|u|p−1u=μ on (−1,1) with boundary condition u(−1)=u(1)=0. We establish some existence and uniqueness results. We examine the limiting behavior of three approximation schemes. The isolated singularity at 0 is also investigated.