Oscillation Criteria for Second-order Nonlinear Self-adjoint Differential Equations

• Autores: M. Hesaaraki, Amir Moradifam
• Localización: Methods and applications of analysis, ISSN 1073-2772, Vol. 13, Nº 4, 2006, págs. 373-386
• Idioma: inglés
• DOI: 10.4310/maa.2006.v13.n4.a4
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• Resumen

  • Our concern is to solve the oscillation problem for the nonlinear self-adjoint equation (a(t)x')' + b(t)g(x) = 0, where g(x) satisfies the Signum condition xg(x) > 0 if x 6= 0, but is not imposed such monotonicity as superlinear or sublinear. The problem has not been solved for the critical cases:

    liminf |x|.0 g(x) x < 1 4 < limsup |x|.0 g(x) x , and liminf |x|.8 g(x) x < 1 4 < limsup |x|.8 g(x) x , which are more difficult, by now. We concentrate our attention on this point and give some answers.

    Sufficient conditions are given for all nontrivial solutions to be oscillatory