Special Issue: Variational and topological analysis: methods and applications
Guest Editors
Calogero Vetro
Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy
Email: calogero.vetro@unipa.it
Shengda Zeng
Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, China
Jagiellonian University in Krakow, Department of Mathematics, Faculty of Mathematics and Computer Science, ul. Lojasiewicza 6, 30-348 Krakow, Poland
Email: zengshengda@163.com
Manuscript Topics
Variational and topological analysis plays a fundamental role in the theory of nonlinear analysis and partial differential equations, inclusions and inequalities. It deals with a variety of theoretical methods and tools to discuss the regularity, existence, multiplicity, blow-up and approximation of solutions. Further, it is at the interface between pure and applied mathematics, indeed many differential equations originate as mathematical models of real systems of interest in contexts like as physics, engineering, control theory, differential geometry, and economics. Special attention is paid to the analysis and regularization of problems with singularities and critical nonlinearities.
The aim of this special issue is to focus on the recent developments in the theory of variational and topological methods that are basically designed for analyzing differential systems and discussing their complex behavior, intrinsic properties, and evolution. Hence it is aimed to provide a platform for reflection and exchange of ideas, to better understand and improve the knowledge.
This special issue is devoted to select original and new papers, as well as survey papers. More precisely, the scope is to cover topics that include bifurcation theory, critical point theory, degree theory, Morse theory, nonlinear elliptic and parabolic equations, inclusions and inequalities, Musielak-Orlicz Sobolev spaces, linear and nonlinear operators, spectral theory, stability analysis of mathematical models.
Potential topics include but are not limited to:
• Existence, stability and asymptotic results to differential equations and systems.
• Existence and extremality results to double phase elliptic inclusions.
• Existence, multiplicity, and regularity of solutions to evolution equations.
• Topological methods for nonlinear problems with convection terms.
• Existence results for quasi-variational-hemivariational inequalities.
• Regularity and numerical approximation of parametric free boundary problems.
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