Study of non local elliptic problems involving variable order and variable exponents

Abstract

In the thesis we study some non local and nonlinear elliptic equations involving variable order and variable exponents For studying these problems we introduce the variable order fractional Sobolev spaces with variable exponents and explore basic properties of these spaces Then we study the existence multiplicity of weak solutions of a class of elliptic equations involving the nonlocal operator with variable order and variable exponents and generalized Choquard type also called Hartree type...