Displaying similar documents to “Periodic problems for ODEs via multivalued Poincaré operators”

Vector integral equations with discontinuous right-hand side

Filippo Cammaroto, Paolo Cubiotti (1999)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the integral equation u ( t ) = f ( ∫ I g ( t , z ) u ( z ) d z ) , with t ∈ I = [ 0 , 1 ] , f : 𝐑 n → 𝐑 n and g : I × I → [ 0 , + ∞ [ . We prove an existence theorem for solutions u ∈ L ∞ ( I , 𝐑 n ) where the function f is not assumed to be continuous, extending a result previously obtained for the case n = 1 .

Non-autonomous vector integral equations with discontinuous right-hand side

Paolo Cubiotti (2001)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the integral equation u ( t ) = f ( t , ∫ I g ( t , z ) u ( z ) d z ) , with t ∈ I : = [ 0 , 1 ] , f : I × ℝ n → ℝ n and g : I × I → [ 0 , + ∞ [ . We prove an existence theorem for solutions u ∈ L s ( I , ℝ n ) , s ∈ ] 1 , + ∞ ] , where f is not assumed to be continuous in the second variable. Our result extends a result recently obtained for the special case where f does not depend explicitly on the first variable t ∈ I .

Periodic solutions for differential inclusions in ℝ N

Michael E. Filippakis, Nikolaos S. Papageorgiou (2006)

Archivum Mathematicum

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We consider first order periodic differential inclusions in ℝ N . The presence of a subdifferential term incorporates in our framework differential variational inequalities in ℝ N . We establish the existence of extremal periodic solutions and we also obtain existence results for the “convex” and “nonconvex”problems.

Nonlinear boundary value problems for differential inclusions y'' ∈ F(t,y,y')

L. H. Erbe, W. Krawcewicz (1991)

Annales Polonici Mathematici

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Applying the topological transversality method of Granas and the a priori bounds technique we prove some existence results for systems of differential inclusions of the form y'' ∈ F(t,y,y'), where F is a Carathéodory multifunction and y satisfies some nonlinear boundary conditions.