Nonautonomous fractional problems with exponential growth

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

Evolution Semigroups for Nonautonomous Cauchy Problems

In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems (NCP ) { u̇(t) = A(t)u(t) u(s) = x ∈ X on a Banach space X by the existence of certain evolution semigroups. Then, we use these generation results for evolution semigroups to derive wellposedness for nonautonomous Cauchy problems under some “concrete” conditions. As a typical example, we discuss the so called “...

Exponential Stability of Nonlinear Nonautonomous Multivariable Discrete Systems

The basic method for the stability analysis of nonlinear time-discrete systems is the Lyapunov functions one, cf. [1,2]. By this method many very strong results are obtained, but finding Lyapunov’s functions is often connected with serious mathematical difficulties. Explicit stability stability conditions for nonlinear multivariable systems are established mainly in the case of autonomous linea...

Pullback Exponential Attractors for Nonautonomous Reaction-Diffusion Equations

Under the assumption that g t ( ) is translation bounded in loc L R L 4 4 ( ; ( )) Ω , and using the method developed in [3], we prove the existence of pullback exponential attractors in H 1 0 ( ) Ω for nonlinear reaction diffusion equation with polynomial growth nonlinearity( p 2 ≥ is arbitrary).

Nonautonomous difference equations: Open problems and conjectures