上下解方法在P-Laplace边值问题上的应用  

The Application of Upper and Lower Solutions in P-Laplace Equation Boundary Value Problems

作　　者：孟宪瑞[1] 佟玉霞[1] 张硕[2] 

机构地区：[1]河北理工大学理学院,唐山063009 [2]天津师范大学津沽学院,天津300387

出　　处：《武汉理工大学学报》2010年第3期173-176,共4页Journal of Wuhan University of Technology

基　　金：河北理工大学科学研究基金(z200916)

摘　　要：研究一类带脉冲边值条件的P-Laplace边值问题解的存在性,主要是将所研究的边值问题转换成等价的积分方程,通过定义上下解构造凸闭集,通过积分方程定义算子,利用算子在凸闭集中的性质证明此算子是单调全连续算子,最后利用Schauder不动点定理得到算子的不动点,从而获得边值问题解的存在性。In this paper,the existence of a solution of p-Laplacian boundary value problems with impulsive effects is investigated.Mainly a integral eguation which is equivalent to the boundary value problem is constructed.A convex closed set is constructed by defining upper and lower solutions.A operator is defined through the integral equation.By the property of the operator in the constructed convex closed set,the Operator is proved that it is monotone and completely continuous.Finally a fixed point of the operator is obtained by Schauder fixed point theorem.Thus the existence of boundary value problems solutions is proved.

关 键 词：上下解 不动点 算子 

分 类 号：O175.8[理学—数学]