Conjugacy and disconjugacy criteria for second order linear ordinary differential equations
Conjugacy and disconjugacy criteria are established for the equation where is a locally summable function.
Conjugacy and disconjugacy criteria are established for the equation where is a locally summable function.
Oscillation properties of the self-adjoint, two term, differential equation are investigated. Using the variational method and the concept of the principal system of solutions it is proved that (*) is conjugate on if there exist an integer and such that and Some extensions of this criterion are suggested.
Sufficient conditions on the function ensuring that the half-linear second order differential equation possesses a nontrivial solution having at least two zeros in a given interval are obtained. These conditions extend some recently proved conjugacy criteria for linear equations which correspond to the case .
We study the generalized half-linear second order differential equation via the associated Riccati type differential equation and Prüfer transformation. We establish a de la Vallée Poussin type inequality for the distance of consecutive zeros of a nontrivial solution and this result we apply to the “classical” half-linear differential equation regarded as a perturbation of the half-linear Euler differential equation with the so-called critical oscillation constant. In the second part of the paper...
The existence of decaying positive solutions in of the equations and displayed below is considered. From the existence of such solutions for the subhomogeneous cases (i.e. as ), a super-sub-solutions method (see § 2.2) enables us to obtain existence theorems for more general cases.
We establish Vallée Poussin type disconjugacy and disfocality criteria for the half-linear second order differential equation , where α ∈ (0,1] and the functions are allowed to have singularities at the end points t = a, t = b of the interval under consideration.