Geodesic
On asymptotic behaviour of solutions with infinite derivative for regular second-order Emden–Fowler type differential equations with negative potential
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 2, pp. 207-214 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we consider the second-order Emden–Fowler 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 non-extensible 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 non-extensible solutions to the equation are obtained. Also the sufficient conditions providing the following solutions' properties $\lim\limits_{x \to a} |y'(x)| = +\infty$, $\lim\limits_{x \to a} |y(x)| <+ \infty,$ where $a < \infty$ is a boundary point, are obtained.
Keywords: second-order Emden–Fowler type differential equations, regular nonlinearity, asymptotic behaviour. 
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K. M. Dulina. On asymptotic behaviour of solutions with infinite derivative for regular second-order Emden–Fowler type differential equations with negative potential. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 2, pp. 207-214. http://geodesic.mathdoc.fr/item/VUU_2016_26_2_a5/

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