On decreasing solutions of second order nearly linear differential equations

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Authors

ŘEHÁK Pavel

Year of publication 2014
Type Article in Periodical
Magazine / Source Boundary Value Problems
MU Faculty or unit

Faculty of Education

Citation
Web http://www.boundaryvalueproblems.com/content/2014/1/62
Doi http://dx.doi.org/10.1186/1687-2770-2014-62
Field General mathematics
Keywords nonlinear second order differential equation; decreasing solution; regularly varying function
Description 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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