On super-linear Emden-Fowler type differential equations

被引：19

作者：

Dosla, Zuzana ^{[1
]}

Marini, Mauro ^{[2
]}

机构：

[1] Masaryk Univ, Dept Math & Stat, CZ-61137 Brno, Czech Republic

[2] Univ Florence, Dept Math & Informat Ulisse Dini, I-50139 Florence, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 416卷 / 02期

关键词：

Second order nonlinear differential equation; Globally positive solution; Intermediate solutions; Oscillatory solution; POSITIVE SOLUTIONS; P-LAPLACIAN; OSCILLATION; NONOSCILLATION;

D O I：

10.1016/j.jmaa.2014.02.052

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the second order Emden-Fowler type differential equation (a (t) vertical bar x'vertical bar sgn x')' + b(t) vertical bar x vertical bar(beta)sgn x = 0 in the super-linear case alpha < beta. 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 of our results are new also for the Emden-Fowler equation. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：497 / 510

页数：14

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