Abstract

In this paper we consider the secondorder EmdenFowler type differential equation with negative potential $y''p(x, y, y') y^k \text{ sgn } y=0$ in case of regular nonlinearity $k>1$. We assume that the function $p(x, u, v)$ is continuous in $x$ and Lipschitz continuous in two last variables. We investigate asymptotic behaviour of nonextensible solutions to the equation above. We consider the case of a positive function $p(x, u, v)$ unbounded from above and bounded away from 0 from below. The conditions guaranteeing an existence of a vertical asymptote of all nontrivial nonextensible solutions to the equation are obtained. Also the sufficient conditions providing the following solutions' properties $\displaystyle \lim_{x \to a} y'(x) = +\infty$, $\displaystyle \lim_{x \to a} y(x) <+ \infty$, where $a < \infty$ is a boundary point, are obtained.

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