三阶奇摄动非线性边值问题

Third Order Nonlinear Singularly Perturbed Boundary Value Problem

Department of Basic Science and Engineering, Dalian Railway Institute, Dalian 116028, P R China

摘要: 利用微分不等式理论,研究了某一类三阶奇摄动非线性边值问题。以二阶边值问题的已知结果为基础,引入Volterra型积分算子,建立了三阶非线性边值问题的上下解方法。在适当条件下,构造出具体的上下解,得出解的存在性和渐进估计。结果表明这种技巧也为三阶奇摄动边值问题的研究提出了崭新的思路。最后举例验证文中定理的正确性。
- 三阶非线性边值问题 /
- 上下解 /
- Volterra型积分算子 /
- 存在性和渐近估计
Abstract: Third order singulary perturbed boundary value problem by means of differential inequality theories is studied.Based on the given results of second order nonlinear boundary value problem,the upper and lower solutions method of third order nonlinear boundary value problems by making use of volterra type integral operat or was established.Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem.An example is given to demonstrate the applications.
- third order boundary value problem /
- upper and lower solutions /
- Volterra tyte integral operator /
- existence and asymptotic estimates

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