A duality approach for solving identification problems related to integrodifferential Maxwell's equations
A fixed Point Theorem and its Applications to Nonlinear Integral Equations in Banach Algebras
A multidimensional identification problem related to a hyperbolic integro-differential equation.
A new characteristic property of Mittag-Leffler functions and fractional cosine functions
A new characteristic property of the Mittag-Leffler function with 1 < α < 2 is deduced. Motivated by this property, a new notion, named α-order cosine function, is developed. It is proved that an α-order cosine function is associated with a solution operator of an α-order abstract Cauchy problem. Consequently, an α-order abstract Cauchy problem is well-posed if and only if its coefficient operator generates a unique α-order cosine function.
A note on integral inclusions in Banach spaces.
A singular perturbation problem in integrodifferential equations.
A stability result for a class of nonlinear integrodifferential equations with L¹ kernels
We study second order nonlinear integro-differential equations in Hilbert spaces with weakly singular convolution kernels obtaining energy estimates for the solutions, uniform in t. Then we show that the solutions decay exponentially at ∞ in the energy norm. Finally, we apply these results to a problem in viscoelasticity.
Abstract nonlinear Volterra integrodifferential equations with nonsmooth kernels
A Cauchy problem for an abstract nonlinear Volterra integrodifferential equation is considered. Existence and uniqueness results are shown for any given time interval under weak time regularity assumptions on the kernel. Some applications to the heat flow with memory are presented.
An abstract inverse problem.
An continuation results for Fredholm integral equations on locally convex spaces.
An existence theorem for Hammerstein integral equations.
An existence theorem for semilinear functional parabolic equations
An existence theorem for the Urysohn integral equation in Banach spaces
An improved exponential decay result for some semilinear integrodifferential equations
We prove exponential decay for the solution of an abstract integrodifferential equation. This equation involves coefficients of polynomial type, weakly singular kernels as well as different powers of the unknown in some norms.
An investigation of convergence and error estimate of approximate solution for a quasilinear parabolic integrodifferential equation
One parabolic integrodifferential problem in the abstract real Hilbert spaces is studied in this paper. The semidiscrete and full discrete approximate solution is defined and the error estimate of Rothe's function in some function spaces is established.
Anti-periodic solutions for second order differential inclusions.
Appendix to the paper: “An existence theorem for the Urysohn integral equation in Banach spaces”
Appendix to the Paper ''Existence Theorems for Lp-solutions of Integral Equations in Banach Spaces''
Application of a trapezoid inequality to neutral Fredholm integro-differential equations in Banach spaces.
Approximation of abstract linear integrodifferential equations
This paper is devoted to the approximation of abstract linear integrodifferential equations by finite difference equations. The result obtained here is applied to the problem of convergence of the backward Euler type discrete scheme.