Weighted Limit Solution of a Nonlinear Ordinary Differential Equation at a Singular Point and Its Property

A singular problem for functional differential equations with decreasing non‐linearities

“…The following theorem gives a kind of general conditions under which Equation (3) has solutions with properties ( 4) and (5). 3) be non-increasing and, moreover, the condition 𝜚g…”

“…for a. e. t ∈ (a, b]. Then for any 𝜆 lying between c and 𝜓(b) problem ( 4), (5), and ( 3) has at least one monotone solution u such that u(b) = 𝜆 and…”

“…had been considered by Emden 1 in 1907. Singular initial value problems for various classes of ordinary differential equations had been studied, for example, in previous studies [2][3][4][5][6] ; for two-point and more general boundary problems for such equations, see previous works 7,8 and references therein. In contrast to the case of ordinary differential equations, significantly less is known for singular equations with argument deviations.…”

“…The theory has a long history; for example, the singular Cauchy problem concerning the equilibrium of a sphere of a polytropic gas had been considered by Emden 1 in 1907. Singular initial value problems for various classes of ordinary differential equations had been studied, for example, in previous studies 2–6 ; for two‐point and more general boundary problems for such equations, see previous works 7,8 and references therein. In contrast to the case of ordinary differential equations, significantly less is known for singular equations with argument deviations 9–16 .…”