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.
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
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
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
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
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
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
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
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
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
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
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.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.