The initial boundary value problem of a mixed-typed hemivariational inequality.
The Kneser property for the abstract Cauchy problem
We establish existence of mild solutions for the semilinear first order functional abstract Cauchy problem and we prove that the set of mild solutions of this problem is connected in the space of continuous functions.
The linearized uniform asymptotic stability of evolution differential equations
The Lyapunov stability of the Timoshenko type equation
The periodic problem for semilinear differential inclusions in Banach spaces
Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness.
The role of an integral inequality in the study of certain differential equations.
The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations
The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated...
The solution set of a differential inclusionon a closed set of a Banach space
We consider differential inclusions with state constraints in a Banach space and study the properties of their solution sets. We prove a relaxation theorem and we apply it to prove the well-posedness of an optimal control problem.
The steepest descent dynamical system with control. Applications to constrained minimization
Let be a real Hilbert space, a convex function of class that we wish to minimize under the convex constraint . A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [5]) applied to the non-smooth function . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function whose critical points coincide with and a control...
The steepest descent dynamical system with control. Applications to constrained minimization
Let H be a real Hilbert space, a convex function of class that we wish to minimize under the convex constraint S. A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [CITE]) applied to the non-smooth function . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function whose critical points coincide with S and...
The Underdetermined Cauchy Problem in Banach Spaces.
The uniform exponential stability of certain linear processes in a Hilbert phase space
The weak Cauchy problem for abstract differential equations
Theorem of differential equations for Mikusinski operators.
Theorem On Differential Equations For Mikusinski Operators
Theory of linear abstract functional differential equations and applications.
Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations.
Time-periodic weak solutions.
To the definition of the global transformation in 2-dimensional linear spaces of continuous functions
Topological properties of solution sets for functional differential inclusions governed by a family of operators.