Some Results On Differential Equations With Integral Boundary Condition

Differential equations is widely used in dynamics, fluid mechanics. The research of differential equations with integral boundary conditions is becoming an important subject. For example, heat conduction, chemical engineering, thermo-elasticity, and population dynamics can be reduced to nonlocal problems with integral bound-ary conditions. For boundary value problems with integral boundary conditions and comments on their importance, we refer the reader to [1-6] and the references therein. With solving these problems, most methods are applied. This paper makes use of cone compression and expansion fixed point theorem, Monch fixed point the-orem to get the existence of positive solutions. The dissertation contains three chapters.Chapter 1 investigates the first-order singular impulsive boundary value prob-lem with integral boundary condition where f(t, u) is singular at u=θ. In this chapter, using cone compression and expansion fixed point theorem, we obtain the existence of positive solutions.In chapter 2, we consider the singular boundary value problem with integral boundary condition where f(t,x) is singular at t=0, t=1, x=θ. Using Monch fixed point theorem, we get the existence of positive solutions in abstract space.In chapter 3, we study the boundary value problem of second order differential equation in infinite space where x'(∞)=(?) x'(t). By using the well-known three functionals fixed point theorem, we obtain the existence of positive solutions.