Elliptic problems with discontinuous nonlinearity has its own difficulties due to the non-differentiability of the associated functional. Hence, a generalized gradient approach developed by Chang has been used to solve such problems if the associated functional is known to be Lipchitz continuous. In this talk, we will consider critical elliptic problem in a bounded domain in $\\mathbb{R}^2$ with the simultaneous presence of a Heaviside type discontinuity and a power-law type singularity and investigate the existence of multiple positive solutions. Here discontinuity coupled with singularity does not fit into any of the known framework and we will discuss our approach employed to obtain positive solutions.

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Last updated: 22 Feb 2019