STUDY THE SOLUTIONS OF HIGHER-ORDER SINGULAR BOUNDARY VALUE PROBLEMS BY VARIATIONAL METHODS

Abstract

This dissertation is devoted to the study of positive solutions for higher-order singular boundary value prob lems using variational methods. The studied problems are: (−1)mu (2m) (x) = λp(x)u(x), x ∈ (0, 1) and (−1)mu (2m) (x) = p(x)f(u(x)), x ∈ (0, 1) with suitable boundary conditions. In the first chapter, we presented some preliminaries from functional analysis and variational methods. In the second chapter, we studied the linear problem and proved the existence of positive solutions using minimization techniques and Green’s function. Finally, in the third chapter, we investigated the nonlinear problem and established existence results by using variational methods and the Mountain Pass Theorem