Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Monotone and oscillatory solution of $y^{(n)}+py=0$


Author: W. J. Kim
Journal: Proc. Amer. Math. Soc. 62 (1977), 77-82
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1977-0425256-8
MathSciNet review: 0425256
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Monotone and oscillatory behaviors of the solutions with the property that $y(x)/{x^2} \to 0$ as $x \to \infty$ or $y(x)/x \to 0$ as $x \to \infty$ are discussed. For example, it is shown that every nonoscillatory solution y, such that $y(x)/x \to 0$ as $x \to \infty$, monotonically tends to zero as $x \to \infty$, provided n is odd, $p \geqq 0$, and ${\smallint ^\infty }{x^{n - 1}}p(x)dx = \infty$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10

Retrieve articles in all journals with MSC: 34C10


Additional Information

Keywords: Monotone and oscillatory solutions, asymptotic behavior, linear equations, ordinary, <I>n</I>th-order, real-valued continuous coefficients
Article copyright: © Copyright 1977 American Mathematical Society