Displaying similar documents to “A note on the theorem on differential inequalities.”

On the dimension of the solution set to the homogeneous linear functional differential equation of the first order

Alexander Domoshnitsky, Robert Hakl, Bedřich Půža (2012)

Czechoslovak Mathematical Journal

Similarity:

Consider the homogeneous equation u ' ( t ) = ℓ ( u ) ( t ) for a.e. t ∈ [ a , b ] where ℓ : C ( [ a , b ] ; ℝ ) → L ( [ a , b ] ; ℝ ) is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.