A class of singularly perturbed evolution systems.
A contribution to the theory of stability of differential equations in Banach space
A dynamical system in a Hilbert space with a weakly attractive nonstationary point
A differential equation is a Hilbert space with all solutions bounded but with so finite nontrivial invariant measure is constructed. In fact, it is shown that all solutions to this equation converge weakly to the origin, nonetheless, there is no stationary point. Moreover, so solution has a non-empty -set.
A functional differential equation in Banach spaces
A global continuation theorem for obtaining eigenvalues and bifurcation points
A Kneser-type theorem for the equation in locally convex spaces.
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 Massera type criterion for a partial neutral functional differential equation.
A multiplicity fixed point theorem in Fréchet spaces.
A necessary and sufficient condition for uniqueness of solutions of singular differential inequalities.
A new a priori estimate for multi-point boundary-value problem.
A non-linear hyperbolic equation.
A note on differential and integral equations in locally convex spaces
A note on the periods of periodic solutions of some autonomous functional differential equations.
A periodic boundary value problem in Hilbert space
In the paper some existence results for periodic boundary value problems for the ordinary differential equation of the second order in a Hilbert space are given. Under some auxiliary assumptions the set of solutions is compact and connected or it is convex.
A principle of linearization in theory of stability of solutions of variational inequalities
It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.
A priori estimates for the existence of a solution for a multi-point boundary value problem.
A remark about a Galerkin method
It is shown that the approximating equations whose existence is required in the author's previous work on partially regular weak solutions can be constructed without any additional assumption about the equation itself. This leads to a variation of a Galerkin method.
A second-order impulsive Cauchy problem.
A theorem about Carathéodory's superposition