Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order

J. Jaros, T. Kusano and N. Yoshida

Address. J. Jaros, Department of Mathematical Analysis, Faculty of Mathematics and Physics, Comenius University, 842 48 Bratislava, SLOVAK REPUBLIC

T. Kusano, Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka, 814-0180, JAPAN

N. Yoshida, Department of Mathematics, Faculty of Science, Toyama University, Toyama, 930-8555, JAPAN


Abstract. In the paper a comparison theory of Sturm-Picone type is developed for the pair of nonlinear second-order ordinary differential equations first of which is the quasilinear differential equation with an oscillatory forcing term and the second is the so-called half-linear differential equation. Use is made of a new nonlinear version of the Picone's formula.

AMSclassification. 34C10 .

Keywords. Forced quasilinear differential equation of the second order, nonlinear Picone's identity, Sturmian comparison thorems