Nonlinear, Convex, Nonsmooth, Functional Analysis in Symmetry

Dear Colleagues,

Nonlinear functional analysis is a branch of mathematical analysis that considers nonlinear mappings. This area is very popular mainly because many applications in functional analysis arise naturally in real-world problems. For example, operator theory arises in many applications in quantum mechanics, and new methods and results of functional analysis are now widely applied in mathematical physics, theoretical physics, and other areas of science. One of the main objectives of nonlinear analysis is to study differential and integral equations and nonlinear operators, and a popular area of focus is considering the local approximation of nonlinear operators by taking linear operators into account. As a result, the theory of approximation (in particular, fixed-point principles) and differential and integral calculus for functions that act between Banach space or more generally topological vector spaces are some of the basic tools of nonlinear functional analysis.

The present issue considers:

1. The qualitative study of solutions for nonhomogeneous (difference and differential) equations having a forced term in some particular spaces of vector-valued functions (for example, Lebesgue–Bochner or Orlicz–Bochner spaces);
2. Different integral conditions and their connections with stability of solutions for evolution equations;
3. Connections between Hyers–Ulam stability (for reccurrences and differential equations and dynamical systems) and exponential dichotomy;
4. The qualitative study of partial differential equations from the perspective of groups or semigroups of operators on Banach spaces.

Prof. Constantin Buse
Prof. Donal O'Regan
Prof. Toka Diagana
Guest Editors

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