Ph. Clément

Asymptotic Behavior of Solutions of Nonlinear Volterra Equations with Completely Positive Kernels

We consider the nonlinear Volterra equation \[ ({\text{V}})\qquad u(t) + (b * Au)(t) \ni f(t),\quad0 \leqq t < \infty \] in the general setting

Abstract Linear and Nonlinear Volterra Equations Preserving Positivity

b:[0,\infty ) \to R

Existence and regularity results for an integral equation with infinite delay in a Banach space

a given kernel, A a nonlinear m-accretive operator on a real Banach space

Examples of unbounded imaginary powers of operators

X,f:[0,\infty ) \to X

Schauder estimates for equations with fractional derivatives

a given function and

Perturbation theory for dual semigroups II. Time-dependent perturbations in the sun-reflexive case

*

A Variational approach to a problem of rotating rods

the convolution. We study the existence of positive solutions of (V) and their asymptotic behavior as

On abstract Volterra equations with kernels having a positive resolvent

t \to \infty

MOUNTAIN PASS TYPE SOLUTIONS FOR QUASILINEAR ELLIPTIC INCLUSIONS

, together with estimates of their rates of decay, under physically reasonable assumptions on b, A, f motivated by the problem of heat flow in materials with memory. The concept of complete positivity of the kernel b and its characterization play a crucial role in the analysis.

Hölder Regularity for a Linear Fractional Evolution Equation

Let X be a real or complex Banach space. We study the Volterra equation \[({\text{v}})\qquad u(t) + \int_0^t {a(t - s)Au(s)\,ds} = f(t)\quad (0 \leqq t \leqq T,T > 0),\] where a is a given kernel, A is a bounded or unbounded linear operator from X to X, and f is a given function with values in X. (Of particular importance is the case