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A periodic boundary value problem in Hilbert space

Boris Rudolf — 1994

Mathematica Bohemica

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.

On the generalized boundary value problem

Boris Rudolf — 2000

Archivum Mathematicum

In the paper it is proved that the generalized linear boundary value problem generates a Fredholm operator. Its index depends on the number of boundary conditions. The existence results of Landesman-Lazer type are given as an application to nonlinear problems by using dual generalized boundary value problems.

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