Non local equations existence and multiplicity results

Abstract

The main theme of my thesis is based on non local type elliptic equations In particular existence of infinitely many nontrivial solutions for a class of equations driven by non local integro differential operator mathcal L K with concave convex nonlinearities and homogeneous Dirichlet boundary conditions in smooth bounded domain in mathbb R N is shown Moreover when mathcal L K reduces to the fractional Laplace operator Delta s and the nonlinearity is of critical concave type existence of at least one sign changing solution has been established These are then further generalized to the case of non local equations with p fractional Laplace operator Existence of infinitely many nontrivial solutions for the class of equations with p q fractional Laplace operator and concave critical nonlinearities have also been studied together with existence of multiple nonnegative solutions when nonlinearity is of convex critical type Also in a different project I have studied the existence nonexistence qualitative properties of the positive solutions of non local semilinear elliptic equations with critical and supercritical type nonlinearities These are all joint published works with my supervisor Dr Mousomi Bhakta in series of four papers newline newline