We establish the existence and uniqueness theorems for a linear and a nonlinear fourth-order boundary value problem. The results obtained generalize the results of Usmani [4] and Yang [5]. The methods used are based, in principle, on [3], [5].
@article{bwmeta1.element.bwnjournal-article-apmv67z1p59bwm,
author = {Jolanta Przybycin},
title = {Existence and uniqueness theorems for fourth-order boundary value problems},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {59-64},
zbl = {0885.34023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z1p59bwm}
}
Jolanta Przybycin. Existence and uniqueness theorems for fourth-order boundary value problems. Annales Polonici Mathematici, Tome 66 (1997) pp. 59-64. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z1p59bwm/
[000] [1] M. S. Berger, Nonlinearity and Functional Analysis, Academic Press, New York, 1977. | Zbl 0368.47001
[001] [2] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966. | Zbl 0148.12601
[002] [3] J. Mawhin, Contractive mappings and periodically perturbed conservative systems, Arch. Math. (Brno) 12 (1976), 67-74. | Zbl 0353.47034
[003] [4] R. A. Usmani, A uniqueness theorem for a boundary value problem, Proc. Amer. Math. Soc. 77 (1979), 329-335. | Zbl 0424.34019
[004] [5] Y. Yang, Fourth-order two-point boundary value problems, Proc. Amer. Math. Soc. 104 (1988), 175-180. | Zbl 0671.34016