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一类非线性二阶常微分方程解的多重性

On the Multiplicity of the Solutions of the Nonlinear Second-Order Differential Equation
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摘要 考虑一类二阶非线性常微分方程的边值问题(p(t)u′)′+h(t)f(u)=0,0<t<1和u(0)=u(1)=0。通过引入f(s)/s在∞与0处的极限值,并运用打靶法和相应的Sturm比较定理得到解的多重性定理,推广有关文献中的许多重要结果。 We consider the boundary value problem for nonlinear second-order differential equations of the form {（p（t）u′）′＋h（t）f（u）=0,0〈t〈1 u（0）=u（1）=0 The purpose of this paper is to establish a condition concerning the behavior of the ratio f（s）/s at infinity and zero for the existence of solutions with prescribed nodal properties. Then we prove the multiplicity result for this problem by using the shooting method and generalized Sturm＇s comparison theorem.
作者 朴大雄 贺佳
机构地区 中国海洋大学数学系
出处 《中国海洋大学学报（自然科学版）》 CAS CSCD 北大核心 2007年第6期1039-1044,共6页 Periodical of Ocean University of China
基金 国家自然科学基金项目(10371010)资助
关键词 两点边值问题 打靶法 非线性 two-point boundary value problem shooting method nonlinear
分类号 O175.8 [理学—基础数学]
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参考文献7

  • 1Hartman P. Ordinary Differential Equations [ M]. Birkhauser: Boston, 1982.
  • 2Anton Zettl. Sturm-Liouville Problems [C]. //edited by D. Hinton, P. Schaefer. Marcel Dekker, spectral theory and computational methods of Sturm-Liouville problems, Proceedings of the 1996 Knoxville Barrett Conference, 1997.
  • 3Marta Garcia-Huidobro, Pedro Ublla. Multiplicity of solutions for a class of nonlinear second-order equations [J ]. Nonlinear Analysis, Theory, Method & Applications, 1997. 28(9): 1509-1520.
  • 4王俊禹,高文杰,张中新.Sturm-Liouville边值问题解的非存在性、存在性和多重性结果[J].数学学报（中文版）,2005,48(4):739-746. 被引量：7
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二级参考文献10

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  • 10Erbe L. H., Wang H., On the existence of positive solutions of ordinary differential equations, Proc. Amer.Math. Soc., 1984, 126: 743-748.

共引文献6

中国海洋大学学报（自然科学版）
2007年 第6期

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