Quadratic equations in Banach space, perturbation techniques and applications to Chandrasekhar's and related equations

In this dissertation perturbation techniques are developed, based on the contraction mapping principle which can be used to prove existence and uniqueness for the quadratic equation x = y + lambdaB(x,x) (1) in a Banach space X; here B: XxX→X is a bounded, symmetric bilinear operator, lambda is a positive parameter and y as a subset of X is fixed. The following is the main result. Theorem. Suppose F: XxX→X is a bounded, symmetric bilinear operator and that the equation z = y + lambdaF(z,z) has a solution z/sup */ of sufficiently small norm. Then equation (1) has a unique solution in a certain closed ball centered at z/sup */. Applications. The theorem is applied to the famous Chandrasekhar equation and to the Anselone-Moore system which are of the form (1) above and yields existence and uniqueness for a solution of (1) for larger values of lambda than previously known, as well as more accurate information on the location of solutions