EUDML

Oscillation and nonoscillation criteria for the self-adjoint linear differential equation ${(t^{α} y^{''})}^{''} - \frac{γ_{2, α}}{t^{4 - α}} y = q (t) y, α \notin {1, 3},$ where $γ_{2, α} = \frac{{(α - 1)}^{2} {(α - 3)}^{2}}{16}$ and $q$ is a real and continuous function, are established. It is proved, using these criteria, that the equation ${(t^{α} y^{''})}^{''} - (\frac{γ_{2, α}}{t^{4 - α}} + \frac{γ}{t^{4 - α} {ln}^{2} t}) y = 0$ is nonoscillatory if and only if $γ \leq \frac{α^{2} - 4 α + 5}{8}$ .

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Oscillation and nonoscillation of perturbed higher order Euler-type differential equations.

Oscillation and nonoscillation of solutions to even order self-adjoint differential equations.

Generalized Picone and Riccati inequalities for half-linear differential operators with arbitrary elliptic matrices.

Two-parametric conditionally oscillatory half-linear differential equations.

Linearized Riccati technique and (non-)oscillation criteria for half-linear difference equations.

Comparison theorems for Riccati inequalities arising in the theory of PDEs with $p$ -Laplacian.

Oscillatory properties of fourth order self-adjoint differential equations