Nonoscillation theory for second order half-linear differential equations in the framework of regular variation
Copyright policy )Nonoscillation theory for second order half-linear differential equations in the framework of regular variation
The authors study regularity properties implying nonoscillation of the solutions of the half-linear equation \[ (| y'|^{\alpha- 1}y')'+ q(t)| y|^{\alpha- 1}y= 0 \] with \(\alpha> 0\) and \(q\) positive and continuous on the half-axis \(t\geq 0\). Some necessary and sufficient conditions for the existence of such solutions are presented. The results generalize corresponding ones for the linear equation (when \(\alpha= 1\)) as proved in [\textit{V. Marić}, Regular variation and differential equations. Lecture Notes in Mathematics 1726. Berlin: Springer-Verlag (2000; Zbl 0946.34001)].
- Comenius University Slovakia
- Fukuoka University Japan
- Fukuoka University Japan
- Toyama College Japan
nonoscillation, regularly varying solutions, Growth and boundedness of solutions to ordinary differential equations, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Rate of growth of functions, orders of infinity, slowly varying functions, Asymptotic properties of solutions to ordinary differential equations, half-linear equation
nonoscillation, regularly varying solutions, Growth and boundedness of solutions to ordinary differential equations, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Rate of growth of functions, orders of infinity, slowly varying functions, Asymptotic properties of solutions to ordinary differential equations, half-linear equation
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