Oscillation and non-oscillation criterion for Riemann-Weber type half-linear differential equations

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Year of publication 2016
Type Article in Periodical
Magazine / Source Electronic Journal of Qualitative Theory of Differential Equations
MU Faculty or unit

Faculty of Science

Doi http://dx.doi.org/10.14232/ejqtde.2016.1.59
Field General mathematics
Keywords half-linear equations; Prüfer angle; Riccati equation; oscillation theory; conditional oscillation; oscillation constant; oscillation criterion
Description By the combination of the modified half-linear Prufer method and the Riccati technique, we study oscillatory properties of half-linear differential equations. Taking into account the transformation theory of half-linear equations and using some known results, we show that the analysed equations in the Riemann-Weber form with perturbations in both terms are conditionally oscillatory. Within the process, we identify the critical oscillation values of their coefficients and, consequently, we decide when the considered equations are oscillatory and when they are non-oscillatory. As a direct corollary of our main result, we solve the so-called critical case for a certain type of half-linear non-perturbed equations.
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