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Local subdifferentials and multivariational inequalities in Banach and Frechet spaces

100%

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

Opuscula Mathematica

2008

tom Vol. 28, no. 3

295-311

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.

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

100%

Agarwal R. P. , O'Regan D.

tom Vol. 46, [Z] 2

169-179

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.

Domains of analytic existence in real Frechet spaces

100%

Mauer M.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

tom Vol. 47, no 1

7-19

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.

An existence result for hyperbolic functional differential inclusions

75%

Benchohra M. , Ntouyas S. K.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2002

tom [Z] 42(1)

1-16

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.

On solvability of linear differential equations in Rn

75%

Shkarin S. A.

2005

tom Vol. 38, nr 1

85--99

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.

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

75%

Benchohra M. , Bennihi O. , Ezzinbi K.

Commentationes Mathematicae

2013

tom Vol 53, No. 1

47--59

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.

A class of hypercyclic Volterra composition operators

63%

Herzog G. , Weber A.

2006

tom Vol. 39, nr 2

465-468

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.