We study the second order Emden-Fowler type differential equation in the super-linear case α<β. Using a Holder-type inequality, we resolve the open problem on the possible coexistence on three possible types of nononscillatory solutions (subdominant, intermediate, and dominant solutions). Jointly with this, sufficient conditions for the existence of globally positive intermediate solutions are established. Some our results are new also for the Emden-Fowler equation.
On super-linear Emden-Fowler type differential equations / Z. Dosla; M. Marini. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 416:(2014), pp. 497-510. [10.1016/j.jmaa.2014.02.052]
On super-linear Emden-Fowler type differential equations
MARINI, MAURO
2014
Abstract
We study the second order Emden-Fowler type differential equation in the super-linear case α<β. Using a Holder-type inequality, we resolve the open problem on the possible coexistence on three possible types of nononscillatory solutions (subdominant, intermediate, and dominant solutions). Jointly with this, sufficient conditions for the existence of globally positive intermediate solutions are established. Some our results are new also for the Emden-Fowler equation.
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