Published in Journal of Fixed Point Theory and Applications
For two differentiable maps between two manifolds of possibly different dimensions, the local and global coincidence homology classes are introduced and studied by Bisi-Bracci-Izawa-Suwa (2016) in the framework of Čech-de Rham cohomology. We take up the problem from the combinatorial viewpoint and give some finer results, in particular for the loca...
Published in Journal of Fixed Point Theory and Applications
In this paper, we consider the following Kirchhoff equation with Choquard nonlinearity: 0.1-a+b∫R3|∇u|2dxΔu+V(x)u=∫R3|u(y)|p|x-y|3-αdy|u|p-2u+|u|q-2u,inR3,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsi...
Published in Journal of Fixed Point Theory and Applications
We formulate algebraically solutions to the isotropic Heisenberg ferromagnet, which is an integrable geometric curve flow. The derivation is based on correspondences between this Heisenberg ferromagnet and the nonlinear Schrödinger equation. The existence of solutions to the Cauchy problems of the isotropic Heisenberg ferromagnet with periodic boun...
Published in Journal of Fixed Point Theory and Applications
I give precise iteration formulae for brake orbits in dimension 3 and use these formulae to get some index inequalities for moduli spaces of real pseudoholomorphic curves, which are important to establish real embedded contact homology and real cylindrical contact homology in dimension 3.
Published in Journal of Fixed Point Theory and Applications
We extend to p-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise averaged mappings. Our main contribution is establishing a calculus for these mappings in p-uniformly convex spaces, showing in particular how the property i...
Published in Journal of Fixed Point Theory and Applications
In this paper, we focus on the k-convex solution to the following boundary blow-up k-Hessian equation with the logarithmic nonlinearity and singular weights SkD2u=H(x)uklnuβ>0,inΩ,u=∞,on∂Ω,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \use...
Published in Journal of Fixed Point Theory and Applications
A flow (X, T) induces the flow (2X,T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2^X,T)$$\end{document}. Quasifactors are minimal subsystems of (2X,T)\documentclas...
Published in Journal of Fixed Point Theory and Applications
In this paper, we use the property of compact sets to propose a unified approach to the Nash equilibrium existence in large games. Our main technique is to convert the large game into a game with finitely many players. We shall use the method to prove the existence theorems of Nash equilibria in different games with infinitely many players.
Published in Journal of Fixed Point Theory and Applications
It follows from Browder (Summa Bras Math 4:183–191, 1960) that for every continuous function F:(X×Y)→Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F : (X \times Y) \...
Published in Journal of Fixed Point Theory and Applications
Let f:M→M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f:M\rightarrow M$$\end{document} be a self-map of a compact manifold and n∈N\documentclass[12pt]{minimal} \usep...
