Existence Of Solutions For Impulsive Singular Boundary Value Problems

The thesis is divided into two chapters. In the first chapter, we study the existence of solutions for impulsive singular boundary value problems on the half-line. In the second chapter, we study the existence of solutions for p-Laplacian in some impulsive singular boundary value problems.In the first chapter, we study the impulsive differential equationswith the singular boundary value problemwhere and are increasing about x. f ∈ C( J × Ω × R,R), J, Ω are nonempty open intervals in R, f may be singular at t = 0. In (1.1.2), the limit x(oo) is a constant not previously given, but in (1.1.3) l is a given constant.In the first chapter, we first give the method of upper and lower solutions for (1.1.1); then obtain the existence of solutions to problem (1.1.1); at last we obtain a necessary and sufficient conditions for existence of positive solutions to a class of sublinear impulsive singular boundary value problem by using the theorem which we obtained.In the second chapter, we mainly study the existence of solutions for p-Laplacian impulsive singular boundary value problemwhere , are bounded and increasing about x, and Ik(x) ≥ 0. gcontinuous and may change sign, the singularity may appear at the point f = 0 and u = 0. In this chapter, we first obtain the method of lower and upper solutions for the nonsingular boundary value problem (2.2.1), and then obtain the existence of solutions for (2.1.1) by using the method of lower and upper solutions.