Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second order quasilinear differential equation are presented. These results yield also new conditions guaranteeing the coexistence of oscillatory and nonoscillatory solutions. Our approach is based on the asymptotic representation of solutions by means of a periodic function and of a suitable zero-counting function.
On oscillatory solutions of quasilinear differential equations / M. BARTUSEK; M. CECCHI;Z. DOSLA; M. MARINI. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 320:(2006), pp. 108-120. [10.1016/j.jmaa.2005.06.057]
On oscillatory solutions of quasilinear differential equations
MARINI, MAURO
2006
Abstract
Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second order quasilinear differential equation are presented. These results yield also new conditions guaranteeing the coexistence of oscillatory and nonoscillatory solutions. Our approach is based on the asymptotic representation of solutions by means of a periodic function and of a suitable zero-counting function.
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