具p-Laplace算子的四阶三点边值问题的两个正解  

Two Positive Solutions for Fourth-Order Three-Point p-Laplacian Boundary Value Problems

作　　者：封汉颍[1] 葛渭高[1] 

机构地区：[1]北京理工大学数学系

出　　处：《数学的实践与认识》2007年第24期140-146,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金资助项目(10671012);教育部博士点专项基金资助项目(20050007011)

摘　　要：研究下列具有p-Laplace算子的四阶三点边值问题(p(u″(t)))″+a(t)f(u(t))=0,t∈(0,1),u(0)=ξu(1),u′(1)=ηu′(0),(p(u″(0))′=α1(p(u″(δ))′,p(u″(1))=β1(p(u″(δ)),通过利用Avery-Henderson不动点定理,给出了边值问题存在至少两个正解的充分条件.We study the following fourth-order three-point boundary value problem with p - Laplacian {（φp（u″（t）））″＋a（t）f（u（t））=0,t∈（0,1）,u（0）=ξu（1）,u′（1）=ηu′（0）,（φp（u″（0））′=α1（φp（u″（δ））′,φp（u″（1））=β1（φp（u″（δ））,By means of the fixed point theorem due to Avery and Henderson, Some sufficient conditions are obtained that guarantee the existence ofat least two positive solutions to the above boundary value problem.

关 键 词：边值问题 锥 不动点定理 正解 

分 类 号：O175.8[理学—数学]