论李纳式方程的边值问题

Q3 Mathematics

WSEAS Transactions on Systems and Control Pub Date : 2023-12-06 DOI:10.37394/23203.2023.18.47

A. Kirichuka, F. Sadyrbaev

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引用次数: 0

摘要

研究了广义lisamadard型微分方程和Sturm-Liouville型的两点线性边界条件。考虑了解的存在性和多重性。从上下函数理论出发，证明了在适当条件下的存在性。对于多重性，采用极坐标方法。多重性的结果是基于在平凡解附近的解和在假定为非振荡的特殊解附近的解的行为的比较。后者的存在是必需的。我们还证明，这些条件对于一类比较广泛的方程是满足的。本文构造了一些例子，这些例子由注释和插图提供。

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On Boundary Value Problems for Liénard Type Equation

The generalized Liénard type differential equation is studied together with the two-point linear boundary conditions of the Sturm-Liouville type. The existence and multiplicity of solutions are considered. The existence under suitable conditions is shown to follow from the lower and upper functions theory. For multiplicity, the polar coordinates approach is used. The multiplicity results are based on the comparison between behavior of solutions near the trivial one, and solutions near the special one, which is preassumed to be non-oscillatory. The existence of the latter is required. It is shown also, that these conditions are fulfilled for a relatively broad class of equations. Some examples are constructed, which are supplied by comments and illustrations.

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来源期刊

WSEAS Transactions on Systems and Control Mathematics-Control and Optimization

CiteScore

1.80

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Systems and Control publishes original research papers relating to systems theory and automatic control. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with systems theory, dynamical systems, linear and non-linear control, intelligent control, robotics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.