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On decreasing solutions of second order nearly linear differential equations

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ŘEHÁK Pavel

Druh Článek v odborném periodiku
Časopis / Zdroj Boundary Value Problems
Fakulta / Pracoviště MU

Pedagogická fakulta

Citace
www http://www.boundaryvalueproblems.com/content/2014/1/62
Doi http://dx.doi.org/10.1186/1687-2770-2014-62
Obor Obecná matematika
Klíčová slova nonlinear second order differential equation; decreasing solution; regularly varying function
Popis We consider the nonlinear equation $ (r(t)G(y'))'=p(t)F(y), $ where $r,p$ are positive continuous functions and $F(|\cdot|),G(|\cdot|)$ are continuous functions which are both regularly varying at zero of index one. Existence and asymptotic behavior of decreasing slowly varying solutions are studied. Our observations can be understood at least in two ways. As a nonlinear extension of results for linear equations. As an analysis of the border case (``between sub-linearity and super-linearity'') for a certain generalization of Emden-Fowler type equation.
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