@article{JolantaPrzybycin1995,
abstract = {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.},
author = {Jolanta Przybycin},
journal = {Annales Polonici Mathematici},
keywords = {bifurcation point; bifurcation interval; Leray-Schauder degree; characteristic value; nonlinear eigenvalue problem; Leray-Schauder degree theory; location of the eigenvalues},
language = {eng},
number = {3},
pages = {249-253},
title = {Nonlinear eigenvalue problems for fourth order ordinary differential equations},
url = {http://eudml.org/doc/262442},
volume = {60},
year = {1995},
}
TY - JOUR
AU - Jolanta Przybycin
TI - Nonlinear eigenvalue problems for fourth order ordinary differential equations
JO - Annales Polonici Mathematici
PY - 1995
VL - 60
IS - 3
SP - 249
EP - 253
AB - 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.
LA - eng
KW - bifurcation point; bifurcation interval; Leray-Schauder degree; characteristic value; nonlinear eigenvalue problem; Leray-Schauder degree theory; location of the eigenvalues
UR - http://eudml.org/doc/262442
ER -