论四阶非线性常微分方程边界值问题正解的存在性和唯一性

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2023-12-15 DOI:10.3103/s1066369x23090025

G. E. Abduragimov

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引用次数: 0

摘要

摘要本文研究了一个 4n 阶非线性常微分方程的两点边界值问题，该问题具有同质边界条件。利用著名的 Krasnoselskii 圆锥展开（压缩）定理，得到了所考虑问题正解存在的充分条件。为了证明正解的唯一性，引用了压缩算子原理。最后，举例说明了所获得的唯一可解性充分条件的满足情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a 4nth-Order Nonlinear Ordinary Differential Equation

Abstract

The paper considers a two-point boundary value problem with homogeneous boundary conditions for a single 4nth-order nonlinear ordinary differential equation. Using the well-known Krasnoselskii theorem on the expansion (compression) of a cone, sufficient conditions for the existence of a positive solution to the problem under consideration are obtained. To prove the uniqueness of a positive solution, the principle of compressed operators was invoked. In conclusion, an example is given that illustrates the fulfillment of the obtained sufficient conditions for the unique solvability of the problem under study.

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.