Executive Summary : | This project focuses on fractional elliptic problems with mixed Dirichlet-Neumann boundary conditions, focusing on nonlinearity with singular and critical terms. The project aims to address the failure of classical critical point theory due to the presence of a singular term and the need for special treatment in convergence analysis of sequences in appropriate function spaces. The project will study problems in different stages, including critical Sobolev exponent nonlinearity and Moser-Trudinger exponential type nonlinearity in singular and very singular cases. It will also tackle problems in variable exponent cases, where the operator may be variable exponent type or the nonlinearity may be variable exponent type or both. The project also includes the Kirchhoff problems with mixed Dirichlet-Neumann boundary conditions, which have been extensively studied in the past. |