Conditions for existence of a global strong solution to a class of nonlinear evolution equations in Hilbert space.
Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations
In this paper we summarize an abstract approach to inertial manifolds for nonautonomous dynamical systems. Our result on the existence of inertial manifolds requires only two geometrical assumptions, called cone invariance and squeezing property, and some additional technical assumptions like boundedness or smoothing properties. We apply this result to processes (two-parameter semiflows) generated by nonautonomous semilinear parabolic evolution equations.
Cone-type constrained relative controllability of semilinear fractional systems with delays
The paper presents fractional-order semilinear, continuous, finite-dimensional dynamical systems with multiple delays both in controls and nonlinear function . The constrained relative controllability of the presented semilinear system and corresponding linear one are discussed. New criteria of constrained relative controllability for the fractional semilinear systems with delays under assumptions put on the control values are established and proved. The conical type constraints are considered....
Conjectures sur les équations différentielles -adiques linéaires
Conley index in Hilbert spaces and a problem of Angenent and van der Vorst
In a recent paper [9] we presented a Galerkin-type Conley index theory for certain classes of infinite-dimensional ODEs without the uniqueness property of the Cauchy problem. In this paper we show how to apply this theory to strongly indefinite elliptic systems. More specifically, we study the elliptic system in Ω, in Ω, u = 0, v = 0 in ∂Ω, (A1) on a smooth bounded domain Ω in for "-"-type Hamiltonians H of class C² satisfying subcritical growth assumptions on their first order derivatives....
Continuity properties of solutions of multivalued equations with white noise perturbation.
Continuity versus nonexistence for a class of linear stochastic Cauchy problems driven by a Brownian motion
Let denote the generator of the rotation group in the space , where denotes the unit circle. We show that the stochastic Cauchy problem where is a standard Brownian motion and is fixed, has a weak solution if and only if the stochastic convolution process has a continuous modification, and that in this situation the weak solution has a continuous modification. In combination with a recent result of Brzeźniak, Peszat and Zabczyk it follows that (1) fails to have a weak solution for all...
Continuous dependence for implicit differential equations in Banach spaces.
Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses
In this article on quasidifferential equation with non-fixed time of impulses we consider the continuous dependence of the solutions on the initial conditions as well as the mappings defined by these equations. We prove general theorems for quasidifferential equations from which follows corresponding results for differential equations, differential inclusion and equations with Hukuhara derivative.
Continuous dependence on data for quasiautonomous nonlinear boundary value problems.
Continuous Dependence Results for Subdifferential Inclusions
Continuous selections of set of mild solutions of evolution inclusions.
Continuous selections of solution sets to Volterra integral inclusions in Banach spaces.
Contractivity in the Numerical Solution of Initial Value Problems.
Contribution a la théorie des équations non linéaires dans les espaces de Banach [Book]
Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator
We study a controllability problem for a system governed by a semilinear functional differential inclusion in a Banach space in the presence of impulse effects and delay. Assuming a regularity of the multivalued non-linearity in terms of the Hausdorff measure of noncompactness we do not require the compactness of the evolution operator generated by the linear part of inclusion. We find existence results for mild solutions of this problem under various growth conditions on the nonlinear part and...
Controllability of functional differential systems of Sobolev type in Banach spaces
Sufficient conditions for controllability of partial functional differential systems of Sobolev type in Banach spaces are established. The results are obtained using compact semigroups and the Schauder fixed point theorem. An example is provided to illustrate the results.
Controllability of impulsive quasi-linear fractional mixed Volterra-Fredholm-type integrodifferential equations in Banach spaces.
Controllability of semilinear functional integrodifferential systems in Banach spaces
Sufficient conditions for controllability of semilinear functional integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem.
Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria
It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...