Stability of Volterra system with impulsive effect.
Stabilization of Volterra equations by noise.
Stable oscillations of weakly nonlinear Volterra integro-differential equations.
Survival in a two-dimensional Lotka-Volterra system.
Systems of nonlinear delay integral equations modelling population growth in a periodic environment
In this paper we study the existence and uniqueness of positive and periodic solutions of nonlinear delay integral systems of the type
Systems with hysteresis in the feedback loop : existence, regularity and asymptotic behaviour of solutions
An existence and regularity theorem is proved for integral equations of convolution type which contain hysteresis nonlinearities. On the basis of this result, frequency-domain stability criteria are derived for feedback systems with a linear infinite-dimensional system in the forward path and a hysteresis nonlinearity in the feedback path. These stability criteria are reminiscent of the classical circle criterion which applies to static sector-bounded nonlinearities. The class of hysteresis operators...
Systems with hysteresis in the feedback loop: existence, regularity and asymptotic behaviour of solutions
An existence and regularity theorem is proved for integral equations of convolution type which contain hysteresis nonlinearities. On the basis of this result, frequency-domain stability criteria are derived for feedback systems with a linear infinite-dimensional system in the forward path and a hysteresis nonlinearity in the feedback path. These stability criteria are reminiscent of the classical circle criterion which applies to static sector-bounded nonlinearities. The class of hysteresis operators...
The asymptotic behavior of solutions to singularly perturbed nonlinear integro-differential equations.
The Asymptotic Behaviour of Solutions of Nonlinear Integral Equations.
The blow-up solutions of integral equations
The existence and exponential stability for random impulsive integrodifferential equations of neutral type.
The freezing method for Volterra integral equations in a Banach space.
The generalized Gronwall inequality and its application to periodic solutions of integrodifferential impulsive periodic system on Banach space.
The Local Stability of Positive Solutions to the Hammerstein Equation with a Nonmonotonic Nemytskii Operator.
The nonlocal bistable equation: Stationary solutions on a bounded interval.
Two-sided solutions of linear integrodifferential equations of Volterra type with delay
Uniqueness of solutions to an Abel type nonlinear integral equation on the half line
We consider a convolution-type integral equation u = k ⋆ g(u) on the half line (−∞; a), a ∈ ℝ, with kernel k(x) = x α−1, 0 < α, and function g(u), continuous and nondecreasing, such that g(0) = 0 and 0 < g(u) for 0 < u. We concentrate on the uniqueness problem for this equation, and we prove that if α ∈ (1, 4), then for any two nontrivial solutions u 1, u 2 there exists a constant c ∈ ℝ such that u 2(x) = u 1(x +c), −∞ < x. The results are obtained by applying Hilbert projective metrics....
Аппарат абстрактных дифференциальных уравнений в исследовании интегральных уравнений типа Вольтерра
Асимптотика решения сингулярного интегрального уравнения с малым параметром
К теории верхних и нижних решений и разрешимости кбазилинейных интегро-дифференциальных уравнений