**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**.

**The call for the Schauder Medal prize candidates**

**Call for papers**

The special issue of **Topological Methods in Nonlinear Analysis** will be dedicated to the memory of **Professor Andrzej Granas**, a man of many virtues and an excellent mathematician, whose recent sudden passing at age 89 was acknowledged with much regret and deep sorrow. This loss can hardly be recovered.

Professor Granas has profoundly contributed to the theory of fixed points and applications of topology in the theory of differential equations. His habilitation thesis, *The theory of compact vector fields and someof its applications to topology of functional spaces*, Rozprawy Matematyczne 30, contributed to the resumption of research in global analysis in Poland, a discipline established in the 1930s through the works of Jean Leray and Juliusz P.Schauder.

Professor Granas has greatly contributed to the organisation of the scientific community in Poland and Canada. He set up the Juliusz P. Schauder Center for Nonlinear Studies at the Nicolaus Copernicus University in Toruń and founded TMNA.

The issue will be co-edited by the special guest-editor Kazimierz Gęba and the TMNA Editor-in-Chief Jean Mawhin, who invite submissions of original research papers, surveys or case studies in all areas of nonlinear analysis with a focus on both theory and applications. Submissions will be considered via a peer review process.

**ISSN 1230-3429**

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 2018 = 0.837****.**

**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.