安布罗塞蒂-普罗迪型三阶函数问题的可解性

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-08-23 DOI:10.1016/j.cnsns.2024.108312

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引用次数: 0

摘要

本研究提出了一种安布罗塞蒂-普罗迪（Ambrosetti-Prodi）替代方案，适用于由带有两种函数边界条件的全三阶微分方程构成的函数问题。主要论点基于下解和上解方法，以及 Leray-Schauder 拓扑度理论。我们强调，多重性情况要求变量有不同的增长速度。一个例子说明了结果的适用性，并展示了一种估算参数分岔值的技术。

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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Solvability of functional third-order problems of Ambrosetti–Prodi-type

This work presents an Ambrosetti–Prodi alternative for functional problems composed of a fully third-order differential equation with two types of functional boundary conditions. The discussion of existence and non-existence of solution is obtained in a more general case, and the multiplicity of solution is done with restrictive boundary conditions-

The main arguments are based on the lower and upper solutions method, together with the Leray–Schauder topological degree theory. We stress that the multiplicity situation requires different speed growths on the variables.

An example illustrates the results’ applicability and shows a technique to estimate the bifurcation values of the parameter.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.