This paper was inspired by the works of Chiappinelli ([3]) and Schmitt and Smith ([7]). We study the problem ℒu = λau + f(·,u,u',u'',u''') with separated boundary conditions on [0,π], where ℒ is a composition of two operators of Sturm-Liouville type. We assume that the nonlinear perturbation f satisfies the inequality |f(x,u,u',u'',u''')| ≤ M|u|. Because of the presence of f the considered equation does not in general have a linearization about 0. For this reason the global bifurcation theorem of Rabinowitz ([5], [6]) is not applicable here. We use the properties of Leray-Schauder degree to establish the existence of nontrivial solutions and describe their location. The results obtained are similar to those proved by Chiappinelli for Sturm-Liouville operators.
@article{bwmeta1.element.bwnjournal-article-apmv60z3p249bwm,
author = {Jolanta Przybycin},
title = {Nonlinear eigenvalue problems for fourth order ordinary differential equations},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {249-253},
zbl = {0823.34029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv60z3p249bwm}
}
Jolanta Przybycin. Nonlinear eigenvalue problems for fourth order ordinary differential equations. Annales Polonici Mathematici, Tome 62 (1995) pp. 249-253. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv60z3p249bwm/
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