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- W2081412537 abstract "A number of authors have employed variations of the Waiewski retract method (see [12]) to study second-order boundary value problems. In the area of ordinary differential equations, these include Hukuhara [6, 71, Jackson and Klaasen [8], and Kaplan, Lasota, and Yorke [9]. Bebernes and Kelley [l] have extended the results of Jackson and Klaasen to contingent equations. In this paper, we use a variation of the Waiewski method similar to those developed by Kluczny [ll] and Hukuhara [6] to prove existence theorems for some nth-order boundary value problems, where IZ > 3. Section 2 contains the basic topological results. In Section 3, we show that an existence theorem of Klaasen [lo] extends to nth-order equations under slightly weaker hypotheses. The results of Sections 2 and 3 are brought together in Section 4 to produce existence theorems for a class of boundary value problems. We conclude the paper with an example of a third-order equation from boundary-layer theory. Coppel [2] has also used a topological argument to prove existence for a particular boundary value problem associated with this equation." @default.
- W2081412537 created "2016-06-24" @default.
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- W2081412537 date "1975-05-01" @default.
- W2081412537 modified "2023-10-16" @default.
- W2081412537 title "Some existence theorems for nth-order boundary value problems" @default.
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- W2081412537 doi "https://doi.org/10.1016/0022-0396(75)90086-8" @default.
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