二阶拟线性微分方程组边值问题的三个对称正解  

THREE SYMMETRIC POSITIVE SOLUTIONS FOR SECOND ORDER QUASILINEAR DIFFERENTIAL EQUATION SYSTEMS OF BOUNDARY VALUE PROBLEMS

作　　者：高英 郭彦平[2] 葛渭高[3] 

机构地区：[1]雁北师院数学系,大同037009 [2]河北科技大学理学院,石家庄050018 [3]北京理工大学应用数学系,北京100081

出　　处：《系统科学与数学》2004年第4期513-519,共7页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10371030)山西省教委高科技开发研究基金(200138)河北科技大学校立基金(QD200313)资助课题.

摘　　要：本文讨论二阶拟线性微分方程组边值问题( p(x'))'+a(t),(t,x,y)=0,( q(y'))'+b(t)g(t,x,y)=0,x(0)-B0(x'(0))=x(1)+Bo(x'(1))=0,y(0)-B1(y'(0))=y(1)+B1(y'(1))=0,其中f,g是非负连续的函数.利用五个泛函的不动点定理,赋予f和g一些增长条件保证至少三个对称正解的存在性.In this paper, we study the second order quasilinear differential equation system of boundary value problem ( pp(x'))' + a(t)f(t,x,y) = 0, ( pq(y'))' + b(t)g(t,x,y) = 0, x(0) - B0(x'(0)) = x(1) + B0(x'(1)) = 0, y(0) - B1(y'(0)) = y(1) + B1(y'(1)) = 0, where f, g are continuous and nonnegative functions. Using the five functionals fixed point theorem, growth conditions are imposed on f and g which ensure the existence of at least three positive symmetric solutions.

关 键 词：拟线性 微分方程组 二阶 边值问题 正解的存在性 对称 泛函 保证 连续 

分 类 号：O175.8[理学—数学]