Previous |  Up |  Next


forced quasilinear differential equation of the second order; nonlinear Picone’s identity; Sturmian comparison thorems
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.
[1] El-Sayed, M. A.: An oscillation criterion for forced second order linear differential equation. Proc. Amer. Math. Soc. 118 (1993), 813–817. MR 1154243
[2] Graef, J. R., Rankin, S. M., Spikes, P. W.: Oscillation results for nonlinear functional differential equations. Funkcialaj Ekvacioj 27 (1984), 255–260. MR 0775209
[3] Jaroš, J., Kusano, T.: On forced second order half-linear equations. Proceedings of the Symposium on the structure and methods of functional differential equations, RIMS Kokyuroku 984, Kyoto University, 1997, 191–197 (in Japanese).
[4] Jaroš, J., Kusano, T.: A Picone type identity for second order half-linear differential equations. Acta Math. Univ. Comenianae LXVIII (1999), 137–151. MR 1711081
[5] Jaroš, J., Kusano, T.: Forced superlinear oscillations via Picone’s identity. Acta Math. Univ. Comenianae LXIX (2000), 107–113. MR 1796791
[6] Leighton, W.: Comparison theorems for linear differential equations of second order. Proc. Amer. Math. Soc. 13 (1962), 603–610. MR 0140759 | Zbl 0118.08202
[7] Nasr, A. H.: Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential. Proc. Amer. Math. Soc. 126 (1998), 123–125. MR 1451823 | Zbl 0891.34038
[8] Picone, M.: Sui valori eccezionali di un parametro da cui dipende un’equazione differenziale lineare ordinaria del second ordine. Ann. Scuola Nom. Pisa 11 (1910), 1–141.
[9] Rankin, S. M. III: Oscillation theorems for second order nonhomogeneous linear differential equations. J. Math. Anal. Appl. 53 (1976), 550–553. MR 0402186
Partner of
EuDML logo