On decreasing solutions of second order nearly linear differential equations

0429228 - MÚ 2015 RIV US eng J - Journal Article
Řehák, Pavel
On decreasing solutions of second order nearly linear differential equations.
Boundary Value Problems. -, 21 March (2014), s. 62. ISSN 1687-2770. E-ISSN 1687-2770
Institutional support: RVO:67985840
Keywords : nonlinear second order differential equation * decreasing solution * regularly varying function
Subject RIV: BA - General Mathematics
Impact factor: 1.014, year: 2014
http://www.boundaryvalueproblems.com/content/2014/1/62

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.
Permanent Link: http://hdl.handle.net/11104/0234369