An Index Classification Theory Of Homogenous P-Laplacian Equations And Existence Of Solutions Of Non-homogenous Equations

In this paper we study the index classification theory of homogenous p-Laplacian equations and existence of solutions of non-homogenous equation.In chapter one we state a few usual notations, definitions and basic results in ordinary differential equations and nonlinear analysis.In chapter two, we first investigate the classification of homogenous equations (φp(u'))' q{t)φp(u) = 0,u(0) = 0 = u(1) where p > 1 is fixed, φp(u) = |u|p-2u and q ∈ L (0,1) , and then discuss the existence of solutions for non-homogenous equations. The main method in the classification is a generalized Prufer equation for t ∈ (0,1), where sinp : R - R is a periodic function and cosp t = d/dt sinp t for t ∈ R.