Geodesic
Nonlinear eigenvalue problems for fourth order ordinary differential equations
Annales Polonici Mathematici, Tome 60 (1994) no. 3, pp. 249-253

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap-60-3-249-253
Keywords: bifurcation point, bifurcation interval, Leray-Schauder degree, characteristic value

Jolanta Przybycin 1

1 
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Jolanta Przybycin. Nonlinear eigenvalue problems for fourth order ordinary differential equations. Annales Polonici Mathematici, Tome 60 (1994) no. 3, pp. 249-253. doi: 10.4064/ap-60-3-249-253

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