Lösung einiger Integralgleichungen erster Art. III. Die Fragen der Lösbarkeit
Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces
We use Fourier multiplier theorems to establish maximal regularity results for a class of integro-differential equations with infinite delay in Banach spaces. Concrete equations of this type arise in viscoelasticity theory. Results are obtained for periodic solutions in the vector-valued Lebesgue and Besov spaces. An application to semilinear equations is considered.
New spectral criteria for almost periodic solutions of evolution equations
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...
Nonlinear impulsive Volterra integral equations in Banach spaces and applications.
Nonlinear integrodifferential equations of mixed type in Banach spaces.
Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition
The aim of the present paper is to investigate the global existence of mild solutions of nonlinear mixed Volterra-Fredholm integrodifferential equations, with nonlocal condition. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions.
Nonlinear Volterra integral equation of the second kind and biorthogonal systems.
Nonlocal Cauchy problem for quasilinear integrodifferential equations in Banach spaces.
Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces.
N-th order impulsive integro-differential equations in Banach spaces.
On a Class of Retarded Partial Differential Equations.
On a class of second order integrodifferential equations
On a nonlinear integral equation
On a reliable solution of a Volterra integral equation in a Hilbert space
We consider a class of Volterra-type integral equations in a Hilbert space. The operators of the equation considered appear as time-dependent functions with values in the space of linear continuous operators mapping the Hilbert space into its dual. We are looking for maximal values of cost functionals with respect to the admissible set of operators. The existence of a solution in the continuous and the discretized form is verified. The convergence analysis is performed. The results are applied to...
On an integral operator in the space of functions with bounded variation
On infinite systems of Volterra integral equations in Banach spaces
On integral equations in a Banach space
On integral inclusions of Volterra type in Banach spaces
On non-absolute functional Volterra integral equations and impulsive differential equations in ordered Banach spaces.
On nonconvex valued Volterra integral inclusions in Banach spaces