An existence theorem for an implicit nonlinear evolution equation.
An explicit construction of sunny nonexpansive retractions in Banach spaces.
An index for global Hopf bifurcation in parabolic systems.
An iterative algorithm by viscosity approximation method for mixed equilibrium problems, variational inclusion and fixed point of an infinite family of pseudo-contractive mappings
The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusion problems for inverse strongly monotone mappings and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in the setting of Hilbert spaces. We prove the strong convergence theorem by using the viscosity approximation method for finding the common element of the above four...
Approximating common fixed points of Lipschitzian semigroup in smooth Banach spaces.
Approximation in the sense of Kato for the transport problem.
Approximation of attainable sets of an evolution inclusion of subdifferential type.
Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces.
Asymptotic behavior of solutions of nonlinear functional differential equations.
Attractors of Strongly Dissipative Systems
A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947...
Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains
Let D be a hyperbolic convex domain in a complex Banach space. Let the mapping F ∈ Hol(D,D) be bounded on each subset strictly inside D, and have a nonempty fixed point set ℱ in D. We consider several methods for constructing retractions onto ℱ under local assumptions of ergodic type. Furthermore, we study the asymptotic behavior of the Cesàro averages of one-parameter semigroups generated by holomorphic mappings.
Brief survey of semigroup theory and its applications to evolution problems.
Browder's convergence for uniformly asymptotically regular nonexpansive semigroups in Hilbert spaces.
Cauchy problems in weighted Lebesgue spaces
Global solvability and asymptotics of semilinear parabolic Cauchy problems in are considered. Following the approach of A. Mielke [15] these problems are investigated in weighted Sobolev spaces. The paper provides also a theory of second order elliptic operators in such spaces considered over , . In particular, the generation of analytic semigroups and the embeddings for the domains of fractional powers of elliptic operators are discussed.
Characterization of the generators of semigroups which leave a convex set invariant
Comment on “A strong convergence of a generalized iterative method for semigroups of nonexpansive mappings in Hilbert spaces”.
Common fixed points for Lipschitzian semigroups.
Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces.
Compact attractor for weakly damped driven Korteweg-de Vries equations on the real line
We investigate the long-time behaviour of solutions to the Korteweg-de Vries equation with a zero order dissipation and an additional forcing term, when the space variable varies over , and prove that it is described by a maximal compact attractor in .
Compact attractors for time-periodic age-structured population models.