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计算一类非线性微分方程的正解

A Numerical Algorithm for Finding Positive Solutions of Nonlinear Differential Equation
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摘要 采用拟弧长延拓的数值算法,计算了一类带有Dirichlet边界条件的非线性微分方程的多个正解,并在一维空间中的两点边值完成了数值实验,数值实验结果与上下解方法得到的理论结果比对,进一步表明非线性微分方程正解的多解的存在性.回答了文献[4]的问题. The numerically positive solutions of the differential equation with Diriehlet boundary condition were investigated in this paper. Compared with sub - super solution method, the existence of numerical Poly - solutions was proved.
作者 朱海龙 李昭祥
机构地区 安徽财经大学统计与应用数学学院 上海师范大学数学系
出处 《佳木斯大学学报（自然科学版）》 CAS 2010年第3期475-477,484,共4页 Journal of Jiamusi University：Natural Science Edition
基金 安徽省优秀青年基金(2009SQRZ083) 安徽省自然科学基金项目(KJ2009B076Z) 上海市重点学科建设项目(S30405) 安徽财经大学科研项目(ACKYQ1065ZC)
关键词 正解 非线性凹凸型问题 上下解方法 拟弧长方法 positive solution concave - convex nonlinearity sub - super solution method pseudo arc length method.
分类号 O175.25 [理学—基础数学]
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参考文献14

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二级参考文献11

  • 1杨忠华,李业忠.求解非线性椭圆型方程边值问题的分歧方法[J].上海师范大学学报（自然科学版）,2005,34(2):17-20. 被引量：5
  • 2Shuang-jie Peng.Multiple Boundary Concentrating Solutions to Dirichlet Problem of Hénon Equation[J].Acta Mathematicae Applicatae Sinica,2006,22(1):137-162. 被引量：4
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  • 10Zhang L. Uniqueness of positive solutions of semilinear elliptic equations. J Differential Equations, 1995, 115: 1-23

共引文献7

佳木斯大学学报（自然科学版）
2010年 第3期

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