具有完全非线性项的非局部梁方程正解

数学物理学报 ›› 2024, Vol. 44 ›› Issue (3): 621-636.

具有完全非线性项的非局部梁方程正解

郭致远,高源,孙家成,张国伟^*()

东北大学数学系沈阳 110819

收稿日期:2022-12-14 修回日期:2023-12-19 出版日期:2024-06-26 发布日期:2024-05-17
通讯作者: *张国伟, Email：gwzhang@mail.neu.edu.cn; gwzhangneum@sina.com

Positive Solutions of Nonlocal Beam Equations with Fully Nonlinear Terms

Guo Zhiyuan,Gao Yuan,Sun Jiacheng,Zhang Guowei^*()

Department of Mathematics, Northeastern University, Shenyang, 110819

Received:2022-12-14 Revised:2023-12-19 Online:2024-06-26 Published:2024-05-17

摘要/Abstract

摘要：

该文研究了两类具有完全非线性项的梁方程, 其边值条件含有 Stieltjes 积分, 应用 Gronwall 型不等式给出三阶导数项的先验估计, 通过在适当开集中的不动点指数方法, 获得了正解的存在性结论. 非线性项中的三阶导数具有二次增长.

关键词: 正解, 不动点指数, 锥, Gronwall 不等式

Abstract:

Two classes of beam equations with fully nonlinear terms are studied that the boundary conditions involve Stieltjes integrals. An a priori bound on the third-order derivative term is evaluated by using a Gronwall -type inequality, and the existence of positive solutions is obtained based on the theory of fixed-point index on suitable open sets. The third-order derivative terms in nonlinearities have quadratic growth.

Key words: Positive solution, Fixed point index, Cone, Gronwall inequality

中图分类号:

O175.14

郭致远, 高源, 孙家成, 张国伟. 具有完全非线性项的非局部梁方程正解[J]. 数学物理学报, 2024, 44(3): 621-636.

Guo Zhiyuan, Gao Yuan, Sun Jiacheng, Zhang Guowei. Positive Solutions of Nonlocal Beam Equations with Fully Nonlinear Terms[J]. Acta mathematica scientia,Series A, 2024, 44(3): 621-636.

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