We consider the second order differential equation (a(t)|x′|^{α}sgn x′)′+b(t)|x|^{β}sgn x=0. in the super-linear case α<β. We prove the existence of the so-called intermediate solutions and we discuss their coexistence with other types of nonoscillatory and oscillatory solutions. Our results are new even for the Emden-Fowler equation (α=1).
Monotonicity conditions in oscillation to superlinear differential equations / Dosla, Zuzana; Marini, Mauro. - In: ELECTRONIC JOURNAL ON THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS. - ISSN 1417-3875. - ELETTRONICO. - 54:(2016), pp. 1-13. [10.14232/ejqtde.2016.1.54]
Monotonicity conditions in oscillation to superlinear differential equations
MARINI, MAURO
2016
Abstract
We consider the second order differential equation (a(t)|x′|^{α}sgn x′)′+b(t)|x|^{β}sgn x=0. in the super-linear case α<β. We prove the existence of the so-called intermediate solutions and we discuss their coexistence with other types of nonoscillatory and oscillatory solutions. Our results are new even for the Emden-Fowler equation (α=1).
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