Bedřich Půža

On boundary value problems for systems of linear functional differential equations

For systems of linear functional differential equations (L FDE) we investigate the boundary value problems (BVP) both on a finite interval and on the real axis. We consider on a finit interval the BVPs for general system of L FDE and for system of linear ordinary differential equations with deviating argument (L ODE with DA): the Fredholmity and representation of solutions by Greens formula, the sign properties of a solution and prove the theorems of differential inequalities, the optimal, in a certain sense, conditions for the unique solvability (all the results are concretized for the initial, multi-point and periodic problems), the teorems on the well-possedness of above problems. For systems of L FDE and ODE with DA we consider the problems on existence of a periodic solution with a prescribed period and existence and unique existence of a bounded solution.

Upper and Lower Solutions of Boundary Value Problems for Functional Differential Equations and Theorems on Functional Differential Inequalities

Abstract Sufficient conditions are found for the existence of an upper and a lower solutions of the boundary value problem where and are linear bounded operators, and and are continuous, generally speaking nonlinear, operators. Kamke type theorems are proved on functional differential inequalities.

On periodic solutions of first order linear functional differential equations

New optimal sufficient conditions are established for the existence of a unique periodic solution of first order scalar functional differential equations

On periodic solutions of higher-order functional differential equations.

For higher-order functional differential equations and, particularly, for nonautonomous differential equations with deviated arguments, new sufficient conditions for the existence and uniqueness of a periodic solution are established.

On the Periodic Boundary Value Problem for First-Order Functional-Differential Equations

V clanku jsou nalezeny efektivni podminky zarucujici řesitelnost periodicke ulohy pro funkcionalni diferencialni rovnice prvniho řadu.

Multi-point boundary value problems for linear functional-differential equations

Abstract Efficient conditions guaranteeing the solvability of multi-point boundary value problems for linear functional-differential equations are established in this paper. The results are proved using the theorems on functional-differential inequalities.

Weighted Cauchy problem for nonlinear singular differential equations with deviating arguments

For higher-order nonlinear differential equations with deviating arguments and with nonintegrable singularities with respect to the time variable, we establish sharp sufficient conditions for the Cauchy problem to be solvable and well-posed.