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| 2α u ) + |u| p−1 u = 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.

Nonlinear elliptic equations with integro-differential divergence form operators and measure data under sign condition on the nonlinearity

“…Since then the research on equations of the form (1.2) has flourished once more, mostly with A being the Dirichlet Laplacian or Dirichlet (rarely regional) fractional Laplacian. We limit ourselves to mentioning [3,15,22,38,43,45] in case of Dirichlet Laplacian or divergence form diffusion operators and [16,17,18,35,37] in case of the fractional Laplacian.…”