Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values

Open Mathematics

Veselý Michal¹  Hasil Petr² 

[1] Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, CZ-611 37Brno, Czech Republic;Department of Mathematics, Faculty of Forestry and Wood Technology, Mendel University in Brno, Zemědělská 1, CZ-613 00Brno, Czech Republic;

关键词: half-linear equation;    oscillation theory;    riccati technique;    oscillation constant;    conditional oscillation;    34c10;    34c15;   

DOI  :  10.1515/math-2018-0047

来源: DOAJ

【 摘 要 】

The paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations whose coefficients are given by the products of functions having mean values and power functions. We prove that the studied very general equations are conditionally oscillatory. In addition, we find the critical oscillation constant.

【 授权许可】

Unknown