Differential Equations and Dynamical Systems (Closed)

A topical collection in Axioms (ISSN 2075-1680). This collection belongs to the section "Mathematical Analysis".

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Editor


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Collection Editor
Departamento de Matemática, Escola de Ciências e Tecnologia, Centro de Investigação em Matemática e Aplicações (CIMA), Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
Interests: differential and difference equations; dynamical systems; boundary value problems; topological and variational methods
Special Issues, Collections and Topics in MDPI journals

Topical Collection Information

Dear Colleagues,

Differential equations, dynamical systems, and related topics are rapidly growing research areas, not only in light of the aim to solve interesting open theoretical issues, but also the presentation of different approaches, new methods, and techniques in a huge variety of applications and models in different science and engineering fields.

Their versatility and applicability derive mainly from being able to consider many types of difference; differential, fractional, integro-differential, and abstract equations; or systems of equations. In addition, they can be complemented with a panoply of local or nonlocal, including integral or functional ones, related to global behaviour and variation.

This Topical Collection aims to compile surveys, recent results, and advances on all aspects of differential equations, dynamical systems, boundary value problems, numerical analysis, stability theory, discrete, continuous  and fractional equations, as well as resonant problems and their applications.

Prof. Dr. Feliz Manuel Minhós
Collection Editor

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Keywords

  • ordinary and partial differential equations
  • boundary value problems
  • dynamical systems
  • numerical analysis
  • stability theory

Related Special Issues

Published Papers (2 papers)

2022

13 pages, 302 KiB  
Article
Global Well-Posedness of the Dissipative Quasi-Geostrophic Equation with Dispersive Forcing
by Jinyi Sun and Lingjuan Zou
Axioms 2022, 11(12), 720; https://doi.org/10.3390/axioms11120720 - 12 Dec 2022
Viewed by 1080
Abstract
The dissipative quasi-geostrophic equation with dispersive forcing is considered. By striking new balances between the dispersive effects of the dispersive forcing and the smoothing effects of the viscous dissipation, we obtain the global well-posedness for Cauchy problem of the dissipative quasi-geostrophic equation with [...] Read more.
The dissipative quasi-geostrophic equation with dispersive forcing is considered. By striking new balances between the dispersive effects of the dispersive forcing and the smoothing effects of the viscous dissipation, we obtain the global well-posedness for Cauchy problem of the dissipative quasi-geostrophic equation with dispersive forcing for arbitrary initial data, provided that the dispersive parameter is large enough. Full article
14 pages, 330 KiB  
Article
Bifurcation Results for Periodic Third-Order Ambrosetti-Prodi-Type Problems
by Feliz Minhós and Nuno Oliveira
Axioms 2022, 11(8), 387; https://doi.org/10.3390/axioms11080387 - 7 Aug 2022
Cited by 2 | Viewed by 1316
Abstract
This paper presents sufficient conditions for the existence of a bifurcation point for nonlinear periodic third-order fully differential equations. In short, the main discussion on the parameter s about the existence, non-existence, or the multiplicity of solutions, states that there are some critical [...] Read more.
This paper presents sufficient conditions for the existence of a bifurcation point for nonlinear periodic third-order fully differential equations. In short, the main discussion on the parameter s about the existence, non-existence, or the multiplicity of solutions, states that there are some critical numbers σ0 and σ1 such that the problem has no solution, at least one or at least two solutions if s<σ0, s=σ0 or σ0>s>σ1, respectively, or with reversed inequalities. The main tool is the different speed of variation between the variables, together with a new type of (strict) lower and upper solutions, not necessarily ordered. The arguments are based in the Leray–Schauder’s topological degree theory. An example suggests a technique to estimate for the critical values σ0 and σ1 of the parameter. Full article
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