The solutions of the differential equation L(n)x + a(0)(t)x = 0, where L-n is a disconjugate operator and ao is of one sign, are studied according to their behavior as t --> infinity. We prove equivalence theorems between solutions of this equation and its adjoint in terms of property A and property B. These theorems generalize the results known for n = 3 and for odd order binomial equations. Some applications are given too.
Equivalency for disconjugate operators / M. CECCHI;Z. DOSLA; M. MARINI. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - STAMPA. - 227:(2001), pp. 19-31. [10.1002/1522-2616(200107)227:1<19::AID-MANA19>3.0.CO;2-5]
Equivalency for disconjugate operators
MARINI, MAURO
2001
Abstract
The solutions of the differential equation L(n)x + a(0)(t)x = 0, where L-n is a disconjugate operator and ao is of one sign, are studied according to their behavior as t --> infinity. We prove equivalence theorems between solutions of this equation and its adjoint in terms of property A and property B. These theorems generalize the results known for n = 3 and for odd order binomial equations. Some applications are given too.
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