一类含一阶导数项二阶微分边值问题单调增加正解的存在性Q1 Q1.PDF

36 / 2 / 河北师范大学学报/ / Vol. 36 No. 2 2012 3 JOURNALOFHEBEI NORMAL UNIVERSITY/ Natural Science Edition/ Ma r. 2012 一类含一阶导数项二阶微分边值问题 X 单调增加正解的存在性 1 2 相秀芬 , 葛渭高 ( 1. , 067000; 2. , 100081) :-, ,. :; ; - ; :O 175.8 :A : 1000-5854(2012) 02-0121-05 Existence of Increasing Positive Solutions of a Class of Second-order Differential Boundary Value Problems with First-order Derivative erm 1 2 XIANG Xiufen , GE Weigao ( 1. epartment of Mathematics and Physics, Chengde Petroleum College,Hebei Chengde 067000,China; ( 2. Collegeof Sciences, Beijing Institute of Technology, Beijing 100081,China) Abstract:By using the norm type cone expansion-expression fixed point theorem,the existenceof increasing positive solutions is studied of a class of second-order nonlinear ordinary differential equations with the first-order derivative term under the integral boundary conditions.A group of sufficient conditions areobtained for the exis- tance of at least one increasing positive solutions. Key words:second-order differential boundary value problem; integral boundary condition; fixed-point the- orem in cones expansion-expression; increasing positive solution , , ., [ 1-6] . [ 1-5] . , x d( t) - Lxc( t ) = K( t)f ( t, x ( t) , xc( t ) ) , 0 t 1, 1 ( 1) x ( 0) - axc( 1) = 0, xc( 0) = x ( t)