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Zbl 0562.34010
Mawhin, Jean
Boundary value problems with nonlinearities having infinite jumps.
(English)
[J] Commentat. Math. Univ. Carol. 25, 401-414 (1984). ISSN 0010-2628

By means of a continuation theorem of Leray-Schauder type an existence theorem for the abstract boundary value problem $L(x)(t)=f(t,x(t),x'(t),...,x\sp{(k)}(t))$, $t\in [a,b]$ 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 {\it L. Aguinaldo} and {\it K. Schmitt} [Proc. Am. Math. Soc. 68, 64-68 (1978; Zbl 0385.34005)] as well as of {\it B. Alfonso Castro} [ibid. 79, 207-211 (1980; Zbl 0439.34021)].
[V.Seda]
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE
47J25 Methods for solving nonlinear operator equations (general)

Keywords: Leray-Schauder method; Applications

Citations: Zbl 0385.34005; Zbl 0439.34021

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