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