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Existence and Properties of Semi-Bounded Global Solutions to the Functional Differential Equation with Volterra's Type Operators on the Real Line | | Maitere Aguerrea
; Robert Hakl
; | | Date: |
30 Jul 2015 | | Abstract: | Consider the equation $$
u’(t)=ell_0(u)(t)-ell_1(u)(t)+f(u)(t)qquadmbox{for~a.~e.~},tinmathbb{R}
$$ where $ell_i:C_{loc}ig(mathbb{R};mathbb{R}ig) o
L_{loc}ig(mathbb{R};mathbb{R}ig)$ $(i=0,1)$ are linear positive
continuous operators and $f:C_{loc}ig(mathbb{R};mathbb{R}ig) o
L_{loc}ig(mathbb{R};mathbb{R}ig)$ is a continuous operator satisfying the
local Carath’eodory conditions. The efficient conditions guaranteeing the
existence of a global solution, which is bounded and non-negative in the
neighbourhood of $-infty$, to the equation considered are established provided
$ell_0$, $ell_1$, and $f$ are Volterra’s type operators. The existence of a
solution which is positive on the whole real line is discussed, as well.
Furthermore, the asymptotic properties of such solutions are studied in the
neighbourhood of $-infty$. The results are applied to certain models appearing
in natural sciences. | | Source: | arXiv, 1507.8573 | | Services: | Forum | Review | PDF | Favorites | |
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