Oscillation theory of self-adjoint equations and some its applications

Došlý, Ondřej

Displaying similar documents to “Oscillation theory of self-adjoint equations and some its applications”

Oscillation and spectral properties of self-adjoint even order differential operators with middle terms.

Došlý, Ondřej (2003)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Oscillation and nonoscillation of higher order self-adjoint differential equations

Ondřej Došlý, Jan Osička (2002)

Czechoslovak Mathematical Journal

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Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation ${(- 1)}^{n} {(t^{α} y^{(n)})}^{(n)} + q (t) y = 0 (*)$ are established. In these criteria, equation $(*)$ is viewed as a perturbation of the conditionally oscillatory equation ${(- 1)}^{n} {(t^{α} y^{(n)})}^{(n)} - \frac{μ_{n, α}}{t^{2 n - α}} y = 0,$ where $μ_{n, α}$ is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed.

Qualitative theory of half-linear second order differential equations

Ondřej Došlý (2002)

Mathematica Bohemica

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Some recent results concerning properties of solutions of the half-linear second order differential equation ${(r (t) Φ (x^{'}))}^{'} + c (t) Φ (x) = 0, Φ (x) : = {| x |}^{p - 2} x, p > 1, (*)$ are presented. A particular attention is paid to the oscillation theory of $(*)$ . Related problems are also discussed.