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1

Semilinear functional differential equations of fractional order with state-dependent delay

Benchohra M., Bennihi O., Ezzinbi K.

Commentationes Mathematicae

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2013

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Vol 53, No. 1

47--59

EN

In this paper we provide sufficient conditions for the existence and uniqueness of mild solutions for a class of semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Frigon- Granas type for contractions maps in Fr´echet spaces combined with -resolvent family is the main tool in our analysis.

2

Local subdifferentials and multivariational inequalities in Banach and Frechet spaces

Kasyanov P. O., Mel'nik V. S., Piccirillo A. M.

Opuscula Mathematica

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2008

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Vol. 28, no. 3

295-311

EN

Some functional-topological concepts of subdifferential and locally subdifferential maps in Frechet spaces are established. Multivariational inequalities with an operator of the pseudomonotone type, connected with subdifferential maps, are considered.

3

A class of hypercyclic Volterra composition operators

Herzog G., Weber A.

Demonstratio Mathematica

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2006

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Vol. 39, nr 2

465-468

EN

We prove that certain Volterra composition operators are hypercyclic on the Frechet space of all continuous functions u : [0,1) ->- R or C with u(0) = 0.

4

Fixed point theory for multimaps defined on closed subsets of Frechet spaces: the projective limit approach

Agarwal R.P., O'Regan D.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2006

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Vol. 46, [Z] 2

169-179

EN

New fixed point results are presented for maps defined on closed subsets of a Fr´echet space E. The proof relies on fixed point results in Banach spaces and viewing E as the projective limit of a sequence of Banach spaces.

5

On solvability of linear differential equations in Rn

Shkarin S. A.

Demonstratio Mathematica

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2005

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Vol. 38, nr 1

85--99

EN

We construct xo is an element of RN and a row-finite matrix T = {Ti,j(t)}i,j is an element of N of polynomials of one real variable t such that the Cauchy problem x(t) = Ttx(t), x{0) = xo in the Frechet space RN has no solutions. We also construct a row-finite matrix A = {Aij(t)}ij is an element of N of C°°(R) functions such that the Cauchy problem x{t) = Atx;(t), x(0) = xo in RN has no solutions for any xo infinity RN\ {0}. We provide some sufficient condition of solvability and unique solvability for linear ordinary differential equations x(t) = Ttx(t) with matrix elements Ti,j(t) analytically dependent on t.

6

An existence result for hyperbolic functional differential inclusions

Benchohra M., Ntouyas S. K.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2002

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[Z] 42(1)

1-16

EN

In this paper we investigate the existence of solutions on an unbounded domain to an hyperbolic differential inclusion in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension to multivalued on locally convex topological spaces, of Schaefer's theorem.

7

Domains of analytic existence in real Frechet spaces

Mauer M.

Bulletin of the Polish Academy of Sciences. Mathematics

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1999

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Vol. 47, no 1

7-19

EN

If E is a real separable Frechet space, we prove that every non void domain Omega of E is open for a continuous semi-norm is a domain of analytic existence. In particular, every non void, open and convex subset Omega of E is a domain of analytic existence. Moreover, this result cannot be improved in the case of an arbitrary real separable Frechet space. In fact, in the space omega of real sequences, a non void domain Omega is a domain of analytic existence if and only if Omega is open for a continuous semi-norm.