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Boundary value problems with nonlinearities having infinite jumps. (English) Zbl 0562.34010
By means of a continuation theorem of Leray-Schauder type an existence theorem for the abstract boundary value problem \(L(x)(t)=f(t,x(t),x'(t),...,x^{(k)}(t))\), \(t\in [a,b]\) is proved, where the kernel of L is spanned by a positive function and f is either bounded below or bounded above. Applications of that theorem extend results of L. Aguinaldo and K. Schmitt [Proc. Am. Math. Soc. 68, 64-68 (1978; Zbl 0385.34005)] as well as of B. Alfonso Castro [ibid. 79, 207-211 (1980; Zbl 0439.34021)].
Reviewer: V.Seda

34B15 Nonlinear boundary value problems for ordinary differential equations
47J25 Iterative procedures involving nonlinear operators
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