Approximation of common solutions to system of mixed equilibrium problems, variational inequality problem, and strict pseudo-contractive mappings.
Approximation of fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces.
Approximation of fixed points of asymptotically pseudocontractive mappings in Banach spaces.
Approximation of fixed points of nonexpansive mappings and solutions of variational inequalities.
Approximation of fixed points of strongly pseudocontractive mappings in uniformly smooth Banach spaces.
Approximation of Operators with Reproducing Nonlinearities.
Approximation of solution branches of nonlinear equations
Approximation of solutions to a system of variational inclusions in Banach spaces.
Approximation solvability of Hammerstein equation.
Approximations of fixed points for mappings in the class .
Approximations of solutions to nonlinear Sobolev type evolution equations.
Approximations to Nonlinear Operator Equations and Newton's Method.
Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity
We show that the critical nonlinear elliptic Neumann problem in , in , on , where is a bounded and smooth domain in , has arbitrarily many solutions, provided that is small enough. More precisely, for any positive integer , there exists such that for , the above problem has a nontrivial solution which blows up at interior points in , as . The location of the blow-up points is related to the domain geometry. The solutions are obtained as critical points of some finite-dimensional...
Asymptotic analysis, existence and sensitivity results for a class of multivalued complementarity problems
In this work we study the multivalued complementarity problem on the non-negative orthant. This is carried out by describing the asymptotic behavior of the sequence of approximate solutions to its multivalued variational inequality formulation. By introducing new classes of multifunctions we provide several existence (possibly allowing unbounded solution set), stability as well as sensitivity results which extend and generalize most of the existing ones in the literature. We also present some kind...
Asymptotic behavior of solutions for linear evolutionary boundary value problem of viscoelastic damped wave equation
We study the existence of global in time and uniform decay of weak solutions to the initial-boundary value problem related to the dynamic behavior of evolution equation accounting for rotational inertial forces along with a linear nonlocal frictional damping arises in viscoelastic materials. By constructing appropriate Lyapunov functional, we show the solution converges to the equilibrium state polynomially in the energy space.
Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity
The asymptotic behaviour for of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress...
Asymptotically pseudocontractions, Banach operator pairs and best simultaneous approximations.
Asymptotically stable almost-periodic oscillations in systems with hysteresis nonlinearities.
Attractors of multivalued semiflows generated by differential inclusions and their approximations.
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...