Abstract.
Our concern is to solve the oscillation problem for the non-linear self-adjoint differential equation (a(t)x’)’+b(t)g(x)=0, where g(x) satisfies the signum condition xg(x)>0 if x≠0, but is not assumed to be monotone. Sufficient conditions and necessary conditions are given for all non-trivial solutions to be oscillatory. The obtained results show that the number 1/4 is a critical value for this problem. This paper takes a different approach from most of the previous research. Proof is given by means of phase plane analysis of systems of Liénard type. Examples are included to illustrate the relation between our theorems and results which were given by Cecchi, Marini and Villari.
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Received: January 5, 2001¶Published online: June 11, 2002
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Sugie, J., Kita, K. & Yamaoka, N. Oscillation constant of second-order non-linear self-adjoint differential equations. Ann. Mat. Pura Appl. IV. Ser. 181, 309–337 (2002). https://doi.org/10.1007/s102310100043
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DOI: https://doi.org/10.1007/s102310100043