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ArticleOriginal scientific text

Title

Existence and uniqueness theorems for fourth-order boundary value problems

Authors 1

Affiliations

  1. Institute of Mathematics, University of Mining and Metallurgy, Mickiewicza 30, 30-059 Kraków, Poland

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].

Keywords

ENG
eigenvalue, Leray-Schauder degree, Fredholm alternative

Bibliography

  1. M. S. Berger, Nonlinearity and Functional Analysis, Academic Press, New York, 1977.
  2. T. Kato, Perturbation Theory for Linear Operators, Springer, 1966.
  3. J. Mawhin, Contractive mappings and periodically perturbed conservative systems, Arch. Math. (Brno) 12 (1976), 67-74.
  4. R. A. Usmani, A uniqueness theorem for a boundary value problem, Proc. Amer. Math. Soc. 77 (1979), 329-335.
  5. Y. Yang, Fourth-order two-point boundary value problems, Proc. Amer. Math. Soc. 104 (1988), 175-180.
Annales Polonici Mathematici
1997/67/1
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Pages:
59-64
Main language of publication
English
Received
1996-02-07
Accepted
1996-08-20
Published
1997
Exact and natural sciences