Existence of Solutions for Differential Equations: Theories, Methods and Applications

Dear Colleagues,

Differential equations are a core research field of applied mathematics, with extensive interdisciplinary applications in natural and social sciences such as physics, engineering, biology and economics. Research on the existence of solutions for differential equations is the fundamental premise for exploring the qualitative and quantitative properties of these solutions and is also the key to solving practical problems by establishing differential equation models. In recent decades, with the development of nonlinear functional analysis, variational methods, topological methods and other disciplines, new breakthroughs have continuously been made in research on the existence of solutions for various types of differential equations, while many key problems in model construction and solution judgment under complex practical scenarios remain to be further explored. Clarifying the conditions for the existence of solutions for different types of differential equations can not only improve the mathematical theoretical system but also provide accurate mathematical modeling and solution support for practical problems in engineering technology and scientific research.

We invite researchers and scholars engaged in researching differential equations, functional analysis and applied mathematics to contribute high-quality original research articles and review articles to this Special Issue. This Special Issue aims to gather the latest research results, innovative methods and cutting-edge application cases in the field of existing solutions for differential equations and to build a high-quality domestic and international academic exchange platform for this field. The research scope of this Special Issue is highly consistent with the core research directions of mathematical journals, and we expect to collect at least five high-quality academic articles.

In this Special Issue, original research articles and reviews are welcome. Research areas include, but are not limited to, the following:

1. Variational methods;
2. Nonlinear functional analysis;
3. Applications of fixed point theory, variational methods and topological degree theory in the existence of solutions for differential equations;
4. Existence of solutions for elliptic partial differential equations;
5. Research on the existence of solutions for fractional differential equations and impulsive differential equations;
6. Applications of the existence theory of differential equation solutions in practical engineering and scientific models.

We look forward to receiving your contributions.

Prof. Dr. Guidong Li
Prof. Dr. Fengjun Li
Dr. Yongyong Li
Guest Editors

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• differential equations
• existence of solutions
• variational methods
• nonlinear functional analysis
• fixed point theory
• topological degree theory
• elliptic partial differential equations
• fractional differential equations