On the question of solvability of the periodic boundary value problem for a system of generalized ordinary differential equations.
Scopo della presente Nota è quello di fornire una maggiorazione della lunghezza dell'intervallo sul quale il problema (1) (2) (3) ammette soltanto la soluzione nulla.
This paper is devoted to the solvability of the Lyapunov equation A*U + UA = I, where A is a given nonselfadjoint differential operator of order 2m with nonlocal boundary conditions, A* is its adjoint, I is the identity operator and U is the selfadjoint operator to be found. We assume that the spectra of A* and -A are disjoint. Under this restriction we prove the existence and uniqueness of the solution of the Lyapunov equation in the class of bounded operators.
2000 Mathematics Subject Classification: 44A40, 44A35A direct algebraic construction of a family of operational calculi for the Euler differential operator δ = t d/dt is proposed. It extends the Mikusiński's approach to the Heaviside operational calculus for the case when the classical Duhamel convolution is replaced by the convolution ...
The one-dimensional steady-state convection-diffusion problem for the unknown temperature of a medium entering the interval with the temperature and flowing with a positive velocity is studied. The medium is being heated with an intensity corresponding to for a constant . We are looking for a velocity with a given average such that the outflow temperature is maximal and discuss the influence of the boundary condition at the point on the “maximizing” function .
Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation are established. In these criteria, equation is viewed as a perturbation of the conditionally oscillatory equation where is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed.
We consider a linear nonautonomous higher order ordinary differential equation and establish the positivity conditions and two-sided bounds for Green’s function for the two-point boundary value problem. Applications of the obtained results to nonlinear equations are also discussed.
We consider linear differential equations of the form on an infinite interval and study the problem of finding those values of for which () has principal solutions vanishing at . This problem may well be called a singular eigenvalue problem, since requiring to be a principal solution can be considered as a boundary condition at . Similarly to the regular eigenvalue problems for () on compact intervals, we can prove a theorem asserting that there exists a sequence of eigenvalues such...