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Resolvent of nonautonomous linear delay functional differential equations

100%

Blot J., Koné M. I.

Nonautonomous Dynamical Systems

2015

tom 2

nr 1

The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

A note on convergence of semigroups

61%

Bobrowski A.

Annales Polonici Mathematici

1998

tom 69

nr 2

107-127

Convergence of semigroups which do not converge in the Trotter-Kato-Neveu sense is considered.

Resolvent Flows for Convex Functionals and p-Harmonic Maps

36%

Kuwae K.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

We prove the unique existence of the (non-linear) resolvent associated to a coercive proper lower semicontinuous function satisfying a weak notion of p-uniform λ-convexity on a complete metric space, and establish the existence of the minimizer of such functions as the large time limit of the resolvents, which generalizing pioneering work by Jost for convex functionals on complete CAT(0)-spaces. The results can be applied to Lp-Wasserstein space over complete p-uniformly convex spaces. As an application, we solve an initial boundary value problem for p-harmonic maps into CAT(0)-spaces in terms of Cheeger type p-Sobolev spaces.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Annales Polonici Mathematici

1 Nonautonomous Dynamical Systems

1 Blot J.

1 Bobrowski A.

1 Koné M. I.

1 Kuwae K.

2 2015

1 1998

Wyniki wyszukiwania

Resolvent of nonautonomous linear delay functional differential equations

A note on convergence of semigroups

Resolvent Flows for Convex Functionals and p-Harmonic Maps