On fourth-order elliptic

boundary value problems

Author:
C. V. Pao

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1023-1030

MSC (1991):
Primary 35J40, 35J65; Secondary 34B15

DOI:
https://doi.org/10.1090/S0002-9939-99-05430-1

Published electronically:
August 3, 1999

MathSciNet review:
1676365

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the existence and uniqueness of a solution for a class of fourth-order elliptic boundary value problems. The existence of a solution is proven by the method of upper and lower solutions without any monotone nondecreasing or nonincreasing property of the nonlinear function. Sufficient conditions for the uniqueness of a solution and some techniques for the construction of upper and lower solutions are given. All the existence and uniqueness results are directly applicable to fourth-order two-point boundary value problems.

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Additional Information

**C. V. Pao**

Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205

Email:
cvpao@eos.ncsu.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05430-1

Keywords:
Fourth-order elliptic equation,
two-point boundary problem,
existence-uniqueness,
method of upper and lower solutions

Received by editor(s):
May 15, 1998

Published electronically:
August 3, 1999

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 2000
American Mathematical Society