# Variational method and conjugacy criteria for half-linear differential equations

## Martin Chvátal and Ondřej Došlý

Address:

Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

E-mail:

xchvatal@math.muni.cz

dosly@math.muni.cz

Abstract: We establish new conjugacy criteria for half-linear second order differential equations. These criteria are based on the relationship between conjugacy of the investigated equation and nonpositivity of the associated energy functional.

AMSclassification: primary 34C10.

Keywords: half-linear differential equation, conjugacy criteria, variational principle, energy functional, half-linear trigonometric functions.

DOI: 10.5817/AM2013-1-9