Topological Methods in Nonlinear Analysis - quarterly international journal is published by the Juliusz Schauder University Centre for Nonlinear Studies with the assistance of the Nicolaus Copernicus University in Toruń.
On March 5, 2019, at the age of 89, Prof. Andrzej Granas, the founder of the Juliusz Schauder Center has passed away. He was an outstanding mathematician and great continuator of Juliusz Schauder's ideas, specialist in non-linear analysis, algebraic topology and fixed points theory. Professor Granas was also the founder and the first Editor In-Chief of the journal Topological Methods in Nonlinear Analysis. His passing was acknowledged with much regret and deep sorrow.
Call for papers
The special issue of Topological Methods in Nonlinear Analysis will be dedicated to the memory of Professor Ioan I. Vrabie, a man of many virtues, an excellent mathematician and author, whose recent sudden passing at age 67 was acknowledged with much regret and deep sorrow. This loss can hardly be retrieved. Professor Vrabie had many profound contributions to a wide range of topics in the theory of infinite dimensional evolution equations and inclusions, nonlinear functional analysis, viability theory and others. He authored several important monographs and textbooks on ordinary and partial differential equations and related topics.
The issue will be co-edited by the special guest-editor Catalin Lefter and Wojciech Kryszewski, who invite submissions of original research papers, surveys or case studies in all areas of differential equations, inclusions, dynamical systems, with a focus on both theory and applications. Submissions will be considered via a peer review process.
TMNA publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those which employ topological methods. Papers in topology which are of interest in nonlinear problems may also be included.
The current impact factors are IF 2017 = 0.645.
The central topics are:
- nonlinear ordinary and partial differential equations and systems, boundary value problems, nonlinear integral equations, equations of mathematical physics;
- differential inclusions, stochastic equations and systems, functional-differential equations, nonlinear analysis methods in discrete mathematics;
- elliptic, parabolic and hyperbolic equations and systems, nonlinear ordinary and partial differential operators, first-order systems,
- Hamilton-Jacobi equations; smooth and topological dynamical systems, flows, dissipativity, ergodicity, nonlinear semigroups; discrete dynamical systems, actions of topological groups with complicated nonlinear dynamics;
- calculus of variations, critical point theory, applications in the theory of differential equations; nonlinear functional and global analysis, equations on manifolds, homotopy methods;
- nonlinear operators and their properties, degree theory, set-valued mappings, topological and metric fixed and periodic point theory;
- convex analysis, game and control theory, optimization, mathematical economics;
- algebraic, computational, applied and differential topology.
Specific areas include the following:
- bifurcation theory, Hopf bifurcation, positive and nodal solutions, periodic solutions, free boundary value problems, heat and wave equations, Schrödinger and Maxwell equations;
- global solutions, finite-time blow up, stability theory, asymptotic behaviour, attractors, invariant manifolds;
- topological and variational methods under the presence of constraints and symmetry;
- theory of topological complexity, abstract and applied homology theory;
- entropy, topological pressure, Hausdorff dimension, notions of mixing;
- symbolic dynamics with emphasis on applications in nonlinear systems;
- vector fields, fixed-point index, measures of noncompactness, Lefschetz and Leray-Schauder theories and their generalizations, Borsuk-Ulam type results, nonlinear spectral theory;
- min-max methods, Lusternik-Schnirelmann and Morse theories, variational problems in physics;
- Navier-Stokes equations, fluid mechanics, liquid crystals, contact mechanics, variational and hemivariational inequalities with applications;
- Markov operators, selections, iterated function systems, algebraic and geometric properties of function spaces, generalized functions;
- Conley index, absolute neighbourhood retracts, Nielsen theory of fixed points, coincidences;
- nonlinear Fredholm and semi-Fredholm operators.