一类P-LAPLACIAN边值问题的多个正解  

Multiple Positive Soluitons of a Class of Boundary Value Problems with P-Laplacian

作　　者：丁卫平[1] 刘玉记[1] 

机构地区：[1]湖南理工学院数学系,湖南岳阳414006

出　　处：《数学的实践与认识》2004年第5期146-152,共7页Mathematics in Practice and Theory

摘　　要：基于 Leggett-Williams在锥上的不动点定理研究两点边值问题(φp( u′( t) ) )′+ a( t) f ( u( t) ) =0　 t∈ ( 0 ,1 )u′( 0 ) =0 ,　αu′( 1 ) + u( 1 ) =0其中 α∈ R,a:( 0 ,1 )→ [0 ,+∞ ) ,f :[0 ,+∞ )→ R,p( z) =| z| p- 2 z。Approach is based on Leggett-Williams fixed point theorem in cones.-For the two-point boundary-values problem(φp(u′(t)))′+a(t)f(u(t))=0 t∈(0,1)u′(0)=0, αu′(1)+u(1)=0 where α∈R, a:(0,1)→[0, +∞), f:[0,+∞)→R+, φp(z)=|z| p-2 z, We give sufficient conditions that guarantee the existence of positive solutions.

关 键 词：P-LAPLACIAN算子 二阶边值问题 LEGGETT-WILLIAMS不动点定理 锥 

分 类 号：O175.8[理学—数学]