Displaying similar documents to “Resolvents, integral equations, limit sets”

On the Volterra integral equation with weakly singular kernel

Stanisław Szufla (2006)

Mathematica Bohemica

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We give sufficient conditions for the existence of at least one integrable solution of equation x ( t ) = f ( t ) + ∫ 0 t K ( t , s ) g ( s , x ( s ) ) d s . Our assumptions and proofs are expressed in terms of measures of noncompactness.

On asymptotic properties of solutions of third order linear differential equations with deviating arguments

Ivan Kiguradze (1994)

Archivum Mathematicum

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The asymptotic properties of solutions of the equation u ' ' ' ( t ) = p 1 ( t ) u ( τ 1 ( t ) ) + p 2 ( t ) u ' ( τ 2 ( t ) ) , are investigated where p i : [ a , + ∞ [ → R ( i = 1 , 2 ) are locally summable functions, τ i : [ a , + ∞ [ → R ( i = 1 , 2 ) measurable ones and τ i ( t ) ≥ t ( i = 1 , 2 ) . In particular, it is proved that if p 1 ( t ) ≤ 0 , p 2 2 ( t ) ≤ α ( t ) | p 1 ( t ) | , ∫ a + ∞ [ τ 1 ( t ) - t ] 2 p 1 ( t ) d t < + ∞ and ∫ a + ∞ α ( t ) d t < + ∞ , then each solution with the first derivative vanishing at infinity is of the Kneser type and a set of all such solutions forms a one-dimensional linear space.