**Abstract**

# Topical Collection "Symmetry in Ordinary and Partial Differential Equations and Applications" (Closed)

A topical collection in *Symmetry* (ISSN 2073-8994). This collection belongs to the section "Mathematics".

## Editor

**Interests:**difference equations; flow invariance; nonlinear regularity theory; ordinary differential equations; partial differential equations; reduction methods; symmetry operators; weak symmetries

Special Issues, Collections and Topics in MDPI journals

## Topical Collection Information

Dear Colleagues,

Ordinary and partial differential equations are universally recognized as powerful tools to model and solve practical problems involving nonlinear phenomena. In particular, we mention physical processes as problems in elasticity theory, where we deal with composites made of two different materials with different hardening exponents.

Therefore, the theory of differential equations has been successfully applied to establish the existence and multiplicity of solutions of boundary value problems via direct methods, minimax theorems, variational methods, and topological methods. If possible, one looks to solutions in special forms by using the symmetries of the driving equation. This also leads to the study of the difference counterparts of such equations to provide exact or approximate solutions. We mention the reduction methods for establishing exact solutions as solutions of lower-dimensional equations. The methods of symmetrization are a key tool in obtaining a priori estimates of solutions to various classes of differential equations, provided that both the involved functions and the data of the problem admit some partial or fully symmetries on the framework space. In particular, comparison principles and method of moving planes up to a critical position, deserve further investigation to prove spherical or axial symmetry results for positive solutions.

This Special Issue aims to collect original and significant contributions dealing with both the theory and applications of differential equations. Also, this Special Issue may serve as a platform for the exchange of ideas between scientists of different disciplines interested in ordinary and partial differential equations and their applications.

Dr. Calogero Vetro*Guest Editor*

**Manuscript Submission Information**

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## Keywords

- difference equations
- flow invariance
- nonlinear regularity theory
- ordinary differential equations
- partial differential equations
- reduction methods
- symmetry operators
- weak symmetries

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