Manuscript Topics

Differential equations, both ordinary (ODEs) and partial (PDEs), are essential in modeling various phenomena across engineering, applied mathematics, and the natural sciences. These equations can be categorized as stationary, describing equilibrium systems, or evolutive, modeling time-dependent processes like wave propagation, diffusion, and reaction-diffusion systems. Stationary equations, often elliptic, arise in fields such as electrostatics and steady-state heat conduction, while evolutive equations, typically parabolic or hyperbolic, are key to dynamic systems in population dynamics, economics, and engineering, as well as biological processes like chemotaxis. The Guest Editors invite original contributions on nonlinear analysis and its applications to both stationary and evolutive differential equations, including PDEs. Submissions exploring the mathematical properties of these equations—such as existence, uniqueness, stability, and regularity—are encouraged, along with those applying nonlinear methods to real-world problems and presenting new models or computational techniques for solving nonlinear differential equations.

The topics include but are not limited to the following:
• Initial-boundary value problems
• Asymptotics and oscillation of solutions
• Global existence of classical solutions and weak solutions
• Blow-up and boundedness of solutions
• Periodicity and stability of solutions
• Long time behavior of solutions
• Numerical simulations of solutions

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