On fourth-order elliptic boundary value problems

Pao, C.

doi:10.1090/S0002-9939-99-05430-1

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: 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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