Asymptotic integrations of nonoscillatory second order differential equations

Author:
Shao Zhu Chen

Journal:
Trans. Amer. Math. Soc. **327** (1991), 853-865

MSC:
Primary 34E10; Secondary 34C99

MathSciNet review:
1028756

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Abstract: The linear differential equation (1) is viewed as a perturbation of the equation (2) , where , and are real-valued continuous functions. Suppose that (2) is nonoscillatory at infinity and , are principal, nonprincipal solutions of (2), respectively. Adapted Riccati techniques are used to obtain an asymptotic integration for the principal solution of (1). Under some mild assumptions, we characterize that (1) has a principal solution satisfying . Sufficient (sometimes necessary) conditions under which the nonprincipal solution of (1) behaves, in three different degrees, like as are also established.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1991-1028756-7

Keywords:
Nonoscillatory equations,
linear perturbations,
asymptotic integrations,
Riccati techniques

Article copyright:
© Copyright 1991
American Mathematical Society