Existence and uniqueness theorems for fourth-order boundary value problems

Jolanta Przybycin

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 1, page 59-64
  • ISSN: 0066-2216

Abstract

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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].

How to cite

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Jolanta Przybycin. "Existence and uniqueness theorems for fourth-order boundary value problems." Annales Polonici Mathematici 67.1 (1997): 59-64. <http://eudml.org/doc/270389>.

@article{JolantaPrzybycin1997,
abstract = {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].},
author = {Jolanta Przybycin},
journal = {Annales Polonici Mathematici},
keywords = {eigenvalue; Leray-Schauder degree; Fredholm alternative; fourth-order boundary value problem; Sturm-Liouville operator},
language = {eng},
number = {1},
pages = {59-64},
title = {Existence and uniqueness theorems for fourth-order boundary value problems},
url = {http://eudml.org/doc/270389},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Jolanta Przybycin
TI - Existence and uniqueness theorems for fourth-order boundary value problems
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 1
SP - 59
EP - 64
AB - 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].
LA - eng
KW - eigenvalue; Leray-Schauder degree; Fredholm alternative; fourth-order boundary value problem; Sturm-Liouville operator
UR - http://eudml.org/doc/270389
ER -

References

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  1. [1] M. S. Berger, Nonlinearity and Functional Analysis, Academic Press, New York, 1977. Zbl0368.47001
  2. [2] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966. Zbl0148.12601
  3. [3] J. Mawhin, Contractive mappings and periodically perturbed conservative systems, Arch. Math. (Brno) 12 (1976), 67-74. Zbl0353.47034
  4. [4] R. A. Usmani, A uniqueness theorem for a boundary value problem, Proc. Amer. Math. Soc. 77 (1979), 329-335. Zbl0424.34019
  5. [5] Y. Yang, Fourth-order two-point boundary value problems, Proc. Amer. Math. Soc. 104 (1988), 175-180. Zbl0671.34016

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