Solvability of Nonlinear Equations with Parameters: Branching, Regularization, Group Symmetry and Solutions Blow-Up

Dear Colleagues,

Starting with the seminal works of A.M. Lyapunov,  A. Poincaré,  and E. Schmidt, the branching theory of nonlinear parameter-dependent equations enabled various essential applications in natural sciences and engineering over the course of the last hundred years. V.I. Yudovich  pioneered the application of symmetry methods in branching theory. A series of applications of the Lyapunov–Schmidt method, Conley index theory, and the central manifold methods in the conditions of group symmetry were reported in many seminal works during the last decades. Various critical processes in plasma physics, fluid dynamics, and thermo-dynamics are modelled using the branching theory of nonlinear differential-operator parameter-dependent equations. The objective of this Special Issue is to report on the cutting edge development of the advanced branching theory of nonlinear equations and their applications. The Special Issue will bring together experts in qualitative theory of differential-operator equations, numerical analysts, and practitioners in the various applied fields of contemporary natural sciences. The results on the solvability of non-standard nonlinear equations with parameters will be reported, focusing on the analysis of the problems associated with branching, regularization, group symmetry, and solution blow-up phenomena.

Prof. Dr. Nikolai A. Sidorov
Guest Editor

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