We discuss a new integral characterization of principal solutions for half-linear differential equations, introduced in the recent paper of S. Fišnarová and R. Mařik, Nonlinear Anal. 74 (2011), 6427--6433 . We study this characterization in the framework of the existing results and we show when this new integral characterization with a parameter α is equivalent with two extremal cases of the integral characterization used in the literature. We illustrate our results on the Euler and Riemann-Weber differential equations.
On the integral characterization of principal solutions for half-linear ODE / Mariella Cecchi; Zuzana Dosla; Ondrej Dosly; Mauro Marini. - In: ELECTRONIC JOURNAL ON THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS. - ISSN 1417-3875. - ELETTRONICO. - 12:(2013), pp. 1-14. [10.14232/ejqtde.2013.1.12]
On the integral characterization of principal solutions for half-linear ODE
CECCHI, MARIELLA;MARINI, MAURO
2013
Abstract
We discuss a new integral characterization of principal solutions for half-linear differential equations, introduced in the recent paper of S. Fišnarová and R. Mařik, Nonlinear Anal. 74 (2011), 6427--6433 . We study this characterization in the framework of the existing results and we show when this new integral characterization with a parameter α is equivalent with two extremal cases of the integral characterization used in the literature. We illustrate our results on the Euler and Riemann-Weber differential equations.
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