Abstract
Consider the equationwhere are linear positive continuous operators and f : Cloc(ℝ;ℝ) → Lloc(ℝ;ℝ) is a continuous operator satisfying the local Carathéodory conditions. Efficient conditions guaranteeing the existence of a global solution, which is bounded and non-negative in the neighbourhood of –∞, to the equation considered are established provided that ℓ0, ℓ1 and f are Volterra-type operators. The existence of a solution that is positive on the whole real line is discussed as well. Furthermore, the asymptotic properties of such solutions are studied in the neighbourhood of –∞. The results are applied to certain models appearing in the natural sciences.
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Schedule a callMore From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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