【作者】 侯传霞；

【导师】 闫宝强；

【作者基本信息】 山东师范大学 ， 应用数学， 2005， 硕士

【摘要】 本文共分两章,在第一章中,我们研究半直线上脉冲微分方程奇异边值问题解的存在性.在第二章中,我们研究一类含有p-Laplacian算子的脉冲奇异边值问题解的存在性. 在第一章中,我们研究脉冲微分方程及奇异边值 x（0）=r,x（∞）=const, （1.1.2） x（0）=r, x’（∞）=l, （1.1.3）其中△x|t=tk =x（t⁺_k）-x（t_k）,△x’|t=t_k =x’（t⁺_k）-x’（t_k）,0<t₁<t₂<…,且lim tk=∞.I_k（x）,I_k（x）∈C（R,R）,且都关于x单增. f∈C（J×Ω×R,R）,J,Ω是R中的非空开集,f可能在t=0点有奇异.在（1.1.2）中极限x（∞）是不事先给定的常数,而（1.1.3）中的l是事先给定的常数. 在第一章中先给出了问题（1.1.1）解存在的上下解方法;然后通过构造上下解,得到解的存在性定理;最后利用这些定理得到了半直线上次线性脉冲奇异边值问题正解存在的充分必要条件. 在第二章中,我们主要研究含有p-Laplacian算子的脉冲奇异边值问题 解的存在性.其中Φ（u）:|u|^p-2u,p>1.△u|t=t_k=u（t⁺_k）-u（t_k）,△Φ（u’）|t=t_k=Φ（u’（t⁺_k））-Φ（u’（t_k））.I_k,I_k∈C（R,R）,有界且都关于x单增,且I_k（x）≥O.g连续且更多还原

【Abstract】 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.更多还原