Functional Differential Equations With Delay and Random Effects

The authors study the existence of mild solutions to a functional differential equation with delay and random effects. They use a random fixed point theorem with a stochastic domain. An example is included to illustrate their results.     

Electron Transfer in the Cs⊂{Mn4Fe4} Cubic Switch: A Soluble Molecular Model of the MnFe Prussian-Blue Analogues

A mixed-valence {Mn^II₃Mn^IIIFe^II₂Fe^III₂} cyanide-bridged molecular cube hosting a caesium cation, Cs⊂{Mn₄Fe₄}, was synthesized and structurally characterized by X-ray diffraction. Cyclic-voltammetry measurements show that its electronic state can be switched between five different redox states, which results in a remarkable electrochromic effect. Magnetic measurements on fresh samples point to the occurrence of a spin-state change near room temperature, which could be ascribed to a metal-to-metal electron transfer converting the {Fe^II−CN−Mn^III} pair into a {Fe^III−CN−Mn^II} pair. This feature was only previously observed in the polymeric MnFe Prussian-blue analogues (PBAs). Moreover, this novel switchable molecule proved to be soluble and stable in organic solvents, paving the way for its integration into advanced materials.     

Impulsive semilinear neutral functional differential inclusions with multivalued jumps

In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed point theorem for the sum of completely continuous and contraction operators.     

Existence results for some partial functional differential equations with state-dependent delay

In this paper, we establish sufficient conditions for the existence of solutions for some partial functional differential equations with state-dependent delay; we assume that the linear part is not necessarily densely defined and satisfies the well-known Hille–Yosida conditions. Our approach is based on a nonlinear alternative of Leray–Schauder type and integrated semigroup theory. An application is provided to a reaction–diffusion equation with state-dependent delay.     

The method of upper and lower solutions and impulsive fractional differential inclusions

In this paper the concept of lower and upper solutions combined with the fixed point theorem of Bohnnenblust–Karlin is used to investigate the existence of solutions for a class of the initial value problem for impulsive differential inclusions involving the Caputo fractional derivative.     

Darboux problem for perturbed partial differential equations of fractional order with finite delay

In this paper we investigate the existence of solutions for functional partial perturbed hyperbolic differential equations with fractional order. These results are based upon a fixed point theorem for the sum of contraction and compact operators.     

Nonconvex-valued impulsive functional differential inclusions with variable times

We use the Schaefer fixed-point theorem, combined with the Bressan-Colombo selection theorem for lower-semicontinuous multivalued operators with nonempty closed and decomposable values, for the investigation of the existence of solutions for first-and second-order impulsive functional differential inclusions with variable times. Published in Neliniini Kolyvannya, Vol. 10, No. 4, pp. 443–463, October–December, 2007.     

Existence results for second order boundary value problem of impulsive dynamic equations on time scales

In this paper, Schaefer's fixed point theorem and nonlinear alternative of Leray-Schauder type are used to investigate the existence of solutions for second order boundary value problem for impulsive dynamic equations on time scales.     

Nondensely defined evolution impulsive differential inclusions with nonlocal conditions

In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined evolution impulsive differential inclusions in Banach spaces with nonlocal conditions.