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| 二阶拟线性微分方程组边值问题的三个对称正解 | |
| 引用本文： | 高英,郭彦平,葛渭高.二阶拟线性微分方程组边值问题的三个对称正解[J].系统科学与数学,2004,24(4):513-519. |
| 作者姓名： | 高英 郭彦平 葛渭高 |
| 作者单位： | 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 |
| 基金项目： | 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. |
| 关 键 词： | 拟线性微分方程组 正解 五个泛函的不动点定理 非线性边界条件 |
| 修稿时间： | 2002年6月5日 |
THREE SYMMETRIC POSITIVE SOLUTIONS FOR SECOND ORDER QUASILINEAR DIFFERENTIAL EQUATION SYSTEMS OF BOUNDARY VALUE PROBLEMS |
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| Ying GAO,Yan Ping GUO,Wei Gao GE.THREE SYMMETRIC POSITIVE SOLUTIONS FOR SECOND ORDER QUASILINEAR DIFFERENTIAL EQUATION SYSTEMS OF BOUNDARY VALUE PROBLEMS[J].Journal of Systems Science and Mathematical Sciences,2004,24(4):513-519. | |
| Authors: | Ying GAO Yan Ping GUO Wei Gao GE |
| Institution: | (1)Department of Mathematics, Yanbei Teacher's College, Datong 037009;(2)College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018;(3)Department of Applied Mathematics,Beijing Institute of Technology,Beijing 100081 |
| Abstract: | 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. |
| Keywords: | Quasilinear differential equation system positive solution the five functionals fixed point theorem nonlinear boundary condition |
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