Accurate solution estimates for nonlinear nonautonomous vector difference equations

Accurate Solution Estimates for Vector Difference Equations

Accurate estimates for the norms of the solutions of a vector difference equation are derived. They give us stability conditions and bounds for the region of attraction of the stationary solution. Our approach is based on estimates for the powers of a constant matrix. We also discuss applications of our main results to partial reaction-diffusion difference equations and to a Volterra difference...

A Priori Solution Estimates for Nonlinear Vector Integral Equations

Nonlinear vector integral equations are considered. Solution estimates and solvability conditions are derived. Applications to the periodic boundary value problem are also discussed. Under some restrictions our results improve the well-known ones. The main tool in the paper is the recent estimates for the resolvent of Hilbert-Schmidt operators.

General Solution of Nonlinear Difference Equations

for ||y || ^ ôo as x tends to infinity in the region Im(x) ^ R0. The coefficients fk(y) are assumed to be holomorphic for ||y|| ;£ 50. Let X, be the eigenvalues of the matrix foy(0). We shall make the following assumptions: (i) /o(0) = 0, (ii)l< |xx|< |x2|< ... < |x„|, (iü)n?=ii^ip,^i^i for j = 1,2, • • -, re and ^UiPi ^ 2, where p, are nonnegative integers. If /o(0) = 0 and X¡ ?¿ 1, we can det...

Integrable Nonautonomous Nonlinear Schrödinger Equations

We show that a recently given nonautonomous nonlinear Schrodinger equation (NLSE) can be transformed into the autonomous NLSE.

Nonautonomous difference equations: Open problems and conjectures