Displaying similar documents to “On the Vallée-Poussin problem for singular differential equations with deviating arguments”

On a criterion for the existence of at least four solutions of functional boundary value problems

Staněk, Svatoslav (1997)

Archivum Mathematicum

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A class of functional boundary conditions for the second order functional differential equation x ' ' ( t ) = ( F x ) ( t ) is introduced. Here F : C 1 ( J ) → L 1 ( J ) is a nonlinear continuous unbounded operator. Sufficient conditions for the existence of at least four solutions are given. The proofs are based on the Bihari lemma, the topological method of homotopy, the Leray-Schauder degree and the Borsuk theorem.

Existence of multiple solutions for some functional boundary value problems

Staněk, Svatoslav (1992)

Archivum Mathematicum

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Let X be the Banach space of C 0 -functions on 〈 0 , 1 〉 with the sup norm and α , β ∈ X → R be continuous increasing functionals, α ( 0 ) = β ( 0 ) = 0 . This paper deals with the functional differential equation (1) x ' ' ' ( t ) = Q [ x , x ' , x ' ' ( t ) ] ( t ) , where Q : X 2 × R → X is locally bounded continuous operator. Some theorems about the existence of two different solutions of (1) satisfying the functional boundary conditions α ( x ) = 0 = β ( x ' ) , x ' ' ( 1 ) - x ' ' ( 0 ) = 0 are given. The method of proof makes use of Schauder linearizatin technique and the Schauder fixed point theorem. The results are modified for 2nd...