Functional differential equations in Banach spaces: Growth and decay of solutions.
Functional differential equations of mixed type in Banach spaces
Functional differential equations of third order.
Functional differential equations with infinite delay in Banach spaces.
Functional differential equations with non-local boundary conditions.
Functional differential equations with nonlocal initial conditions.
Functional differential equations with pulses.
Functional differential inclusions with integral boundary conditions.
Functional differential inequalities with unbounded delay
Classical solutions of functional partial differential inequalities with initial boundary conditions are estimated by maximal solutions of suitable problems for ordinary functional differential equations. Uniqueness of solutions and continuous dependence on given functions are obtained as applications of the comparison result. A theorem on weak functional differential inequalities generated by mixed problems is proved. Our method is based on an axiomatic approach to equations with unbounded delay....
Functional equations of delay type in spaces
Functional evolution equations with nonconvex lower semicontinuous multivalued perturbations.
Functional integro-differential stochastic evolution equations in Hilbert space.
Functional viability theorems for differential inclusions with memory
Functional-differential equations with Riemann-Liouville integrals in the nonlinearities
A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels....
Functionals depending on curvatures and surfaces with curvature measures
Functionals on function and sequence spaces connected with the exponential stability of evolutionary processes
The exponential stability property of an evolutionary process is characterized in terms of the existence of some functionals on certain function spaces. Thus are generalized some well-known results obtained by Datko, Rolewicz, Littman and Van Neerven.
Functionals on sequence spaces connected with the exponential stability of evolutionary processes.
Functions of finite fractional variation and their applications to fractional impulsive equations
We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a -additive term—we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures.
Functions uniformly quiet at zero and existence results for one-parameter boundary value problems
We introduce the notion of uniform quietness at zero for a real-valued function and we study one-parameter nonlocal boundary value problems for second order differential equations involving such functions. By using the Krasnosel'skiĭ fixed point theorem in a cone, we give values of the parameter for which the problems have at least two positive solutions.
Functions without residue and a bilinear differential equation