Publication details

Riccati technique and oscillation constant for modified Euler type half-linear equations


HASIL Petr JAROŠ Jaroslav VESELÝ Michal

Year of publication 2020
Type Article in Periodical
Magazine / Source Publ. Math. Debrecen
MU Faculty or unit

Faculty of Science

Keywords half-linear equation; oscillation theory; non-oscillation; Riccati technique; conditional oscillation; oscillation constant
Description We study equations in a special form with the scalar p-Laplacian for an arbitrarily given number p > 1. It is known that these equations are conditionally oscillatory for some coefficients. The conditional oscillation for certain non-constant coefficients has been proved via the Prüfer angle. Using a new modification of the Riccati method (i.e., by a different approach), we identify easy-to-use conditions on the coefficients which assure the conditionally oscillatory behaviour as well. The obtained results cover equations whose oscillatory properties were not known and these results are new even for linear equations (i.e., for p = 2).
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