On the Urysohn Integral Equation in Locally Convex Spaces
On Volterra-Stieltjes integral equations
Periodic solutions for nonlinear Volterra integrodifferential equations in Banach spaces
In this paper we examine periodic integrodifferential equations in Banach spaces. When the cone is regular, we prove two existence theorems for the extremal solutions in the order interval determined by an upper and a lower solution. Both theorems use only the order structure of the problem and no compactness condition is assumed. In the last section we ask the cone to be only normal but we impose a compactness condition using the ball measure of noncompactness. We obtain the extremal solutions...
Periodic solutions for second order integro-differential equations with infinite delay in Banach spaces
We study the maximal regularity on different function spaces of the second order integro-differential equations with infinite delay (0 ≤ t ≤ 2π) with periodic boundary conditions u(0) = u(2π), u’(0) = u’(2π), where A is a closed operator in a Banach space X, α ∈ ℂ, and a,b ∈ L¹(ℝ₊). We use Fourier multipliers to characterize maximal regularity for (P). Using known results on Fourier multipliers, we find suitable conditions on the kernels a and b under which necessary and sufficient conditions...
Periodic solutions of a class of integrodifferential impulsive periodic systems with time-varying generating operators on Banach space.
Perturbation series and defect correction for the refinement of approximate eigenelements of linear integral operators
Positivity and Regularity of Hyperbolic Volterra Equations in Banach Spaces.
Regularity for solutions of second-order nonlinear integrodifferential functional equations.
Rothe's method to semilinear hyperbolic integrodifferential equations.
Second order linear Volterra integrodifferential equations.
Second order semilinear Volterra integrodifferential equation in Banach space
By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.
Semilinear Volterra integrodifferential equations with nonlocal initial conditions.
Solvability of nonautonomous fractional integrodifferential equations with infinite delay.
Solvability of some integral equations in Hilbert spaces.
Some fixed point theorems and existence of weak solutions of Volterra integral equation under Henstock-Kurzweil-Pettis integrability
In this paper we examine the set of weakly continuous solutions for a Volterra integral equation in Henstock-Kurzweil-Pettis integrability settings. Our result extends those obtained in several kinds of integrability settings. Besides, we prove some new fixed point theorems for function spaces relative to the weak topology which are basic in our considerations and comprise the theory of differential and integral equations in Banach spaces.
Some results for integral inclusions of Volterra type in Banach spaces.
Strong stability and asymptotical almost periodicity of Volterra equations in Banach spaces.
Terminal value problems of impulsive integro-differential equations in Banach spaces.
The abstract renewal equation.
The freezing method for Volterra integral equations in a Banach space.