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On decreasing solutions of second order nearly linear differential equations

Autoři Článek v odborném periodiku Boundary Value Problems http://www.boundaryvalueproblems.com/content/2014/1/62 http://dx.doi.org/10.1186/1687-2770-2014-62 Obecná matematika nonlinear second order differential equation; decreasing solution; regularly varying function 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.