A generalized hybrid steepest-descent method for variational inequalities in Banach spaces.
A generalized iterative algorithm for generalized successively pseudocontractions.
A generalized nonlinear random equations with random fuzzy mappings in uniformly smooth Banach spaces.
A generalized solution to a Cahn-Hilliard/Allen-Cahn system.
A global bifurcation result of a Neumann problem with indefinite weight.
A global description of solutions to nonlinear perturbations of the Wiener--Hopf integral equations.
A global index for bifurcation of fixed points.
A Gregus type common fixed point theorem in normed spaces with applications.
A hybrid extragradient viscosity approximation method for solving equilibrium problems and fixed point problems of infinitely many nonexpansive mappings.
A hybrid iterative scheme for a maximal monotone operator and two countable families of relatively quasi-nonexpansive mappings for generalized mixed equilibrium and variational inequality problems.
A hybrid iterative scheme for equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces.
A hybrid method for monotone variational inequalities involving pseudocontractions.
A hybrid projection algorithm for finding solutions of mixed equilibrium problem and variational inequality problem.
A hybrid-extragradient scheme for system of equilibrium problems, nonexpansive mappings, and monotone mappings.
A la recherche du spectre perdu: An invitation to nonlinear spectral theory
We give a survey on spectra for various classes of nonlinear operators, with a particular emphasis on a comparison of their advantages and drawbacks. Here the most useful spectra are the asymptotic spectrum by M. Furi, M. Martelli and A. Vignoli (1978), the global spectrum by W. Feng (1997), and the local spectrum (called “phantom”) by P. Santucci and M. Väth (2000). In the last part we discuss these spectra for homogeneous operators (of any degree), and derive a discreteness result and a nonlinear...
A linear condition determining local or global existence for nonlinear problems
Given a nonlinear autonomous system of ordinary or partial differential equations that has at least local existence and uniqueness, we offer a linear condition which is necessary and sufficient for existence to be global. This paper is largely concerned with numerically testing this condition. For larger systems, principals of computations are clear but actual implementation poses considerable challenges. We give examples for smaller systems and discuss challenges related to larger systems. This...
A local convergence analysis and applications of Newton's method under weak assumptions.
A local convergence theorem for the inexact Newton method at singular points.
A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid-solid vibration
In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction.
A method for a solution of equilibrium problem and fixed point problem of a nonexpansive semigroup in Hilbert's spaces.