Singular Boundary Value Problems
Abstract
In this dissertation, we are concerned with singular focal boundary value problems. We begin by studying the n^{th} order ordinary differential equationsy^{(n) } + f(x,y,y^',...,y^ {(n2)}) = 0, 0 < x < 1,or y^{(n)} + h(x,y,y^ ',...,y^{(n1)}) = 0, 0 < x < 1,where f(x,y_1,y _2 ,... ,y_{n1}) has singularities at y_{i} = 0, 1 <= i<= n  1, and h(x,y _1{,}y_2,... ,y_{n }) has singularities at y_{i } = 0, 1 <= i<= n. We seek solutions of these differential equations on (0,1), which satisfy homogeneous twopoint focal boundary conditions at x = 0 and x = 1. A fixed point theorem in a cone is applied to appropriate integral operators in order to find the solutions of the boundary value problems. Next, we are concerned with solutions of the n^{th} order differential equationy^{(n)} + psi(x)f(x,y,y ^',...,y^{(n1)}) = 0on the interval (0, 1) satisfying homogeneous twopoint focal boundary value conditions, as well as non homogeneous twopoint focal boundary conditions at x = 0 and x = 1. Different constraints on the function f are assumed depending on whether homogeneous or nonhomogeneous boundary conditions are specified. In both cases, psi (x) has singularities at x = 0, x = 1, and f(x,y _1,y_2 ,... ,y_{n}) has singularities at y_{j} = 0, 1 <= j <= n. Homotopy methods are used to obtain the solutions of these singular boundary value problems.
 Publication:

Ph.D. Thesis
 Pub Date:
 1994
 Bibcode:
 1994PhDT........35Y
 Keywords:

 HOMOTOPY;
 ITERATIONS;
 Mathematics; Physics: Fluid and Plasma; Engineering: System Science