Estimates for the Cauchy function of linear singular differential equations and some applications

Weighted Cauchy problem for nonlinear singular differential equations with deviating arguments

“…Similar results for linear singular differential equations with deviating arguments were obtained in [10]. In the present paper, we generalize the results in [9,10] to Eq. (1.1).…”

“…New and, in a sense, optimal conditions for the unique solvability of the weighted Cauchy problem for linear strongly singular ordinary differential equations of higher order were obtained in [9]. Similar results for linear singular differential equations with deviating arguments were obtained in [10].…”

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

“…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 .…”

“…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.…”