Abstract
The goal of the paper is to investigate the existence of solutions for semilinear upper diagonal infinite systems of differential equations. We will look for solutions of the mentioned infinite systems in a Banach tempered sequence space. In our considerations we utilize the technique associated with the Hausdorff measure of noncompactness and some existence results from the theory of ordinary differential equations in abstract Banach spaces.
Highlights
The principal goal of the paper is to study the solvability of some kind of infinite systems of differential equations
We will investigate semilinear upper diagonal infinite systems of differential equations which are perturbed by nonlinear terms
It is worthwhile mentioning that infinite systems of differential equations can be considered as special cases of ordinary differential equations treated in abstract Banach spaces [5, 7]
Summary
The principal goal of the paper is to study the solvability of some kind of infinite systems of differential equations. Since the sequence space cβ0 is separable we can apply Theorems 3.1 and 3.2 with the assumption that the function f is continuous on the set I1 × B(x0, t). We will consider the semilinear upper diagonal infinite system of differential equations which has the form kn xn = anni (t)xni + fn(t, x1, x2, ...)
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