Existence Of Solutions For Differential System In Banach Spaces

In the first chapter, the existence of solutions of initial value problems for first order integro-differential equations on half-line in Banach spaces is considered.This consideration is resulted from the third section of the third chapter in [1]. This dissertation refers to the measure of noncompactness instead of the Lipschits condition, then obtains the existence of solutions by using Monch fixed point theorem.In the second chapter, we consider the existence of positive solutions of a class singular boundary value problems with impulse in Banach spaces. Using cone fixed point theorem we get the existence of one and two positive solutions.In the third chapter, we investigate singular boundary value problems of coupled system of second and fourth order ordinary differential equations. This system can be seen as the steady state from the nonlinear perturbation model of suspension bridge equations which are presented by Lazer and Mckenna. Differing from both Schauder fixed point theorem in [2] and critical point theory in [3]. this paper gets the existence of two positive solutions by using fixed point theorem of cone expansion and compression.In the last chapter, nonlinear fourth order singular boundary value problems are dealt with. Under the hypothesis of quasi-homogeneous, we obtain the necessary and sufficient conditions for the existence of C~2 and C~3 positive solution respectively.