一类四阶边值问题的多重正解  

Multiple Solutions to a Kind of Fourth-order Boundary Value Problem

作　　者：张琦[1] 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《太原理工大学学报》2009年第6期648-650,656,共4页Journal of Taiyuan University of Technology

基　　金：国家自然科学基金资助项目(10771128)

摘　　要：讨论了一类四阶两点边值问题的多重正解。当非线性项满足一定的条件时,利用Green’s函数的性质将问题转化为求一个全连续算子在一个特殊锥上的不动点的存在性问题。通过利用不动点指数理论及一个新的三解定理,得到了边值问题多个正解的存在性。A kind of fourth-order two-point boundary value problem was considered. When the nonlinear term satisfies certain conditions, by using the property of the Green＇s function, the problem was transformed to the existence of fixed points of a completely continuous operator in a special cone. By using the fixed point theory and a new three-solution theorems, the existence of multiple solutions of the boundary value problem was obtained. A new method was established to consider this kind of problem.

关 键 词：不动点指数 全连续算子 三解定理 

分 类 号：O175.8[理学—数学]