On non-extensible solutions to second-order Emden–Fowler type differential equations with negative potential

Second-order Emden–Fowler type differential equations with regular nonlinearity and bounded negative potential depending on an independent variable, the solution and its first derivative are considered. The results on the existence of asymptotes of nontrivial solutions and estimates of the distance from the initial point to left and right asymptotes positions are given. Continuous dependence of the positions of left and right asymptotes of nontrivial solutions is obtained. The existence of a non-extensible solution with prescribed domain is proved.