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Fourth-order two-point boundary value problems. (English) Zbl 0671.34016
Uniqueness and existence theorems for a linear and a nonlinear fourth- order boundary value problem at nonresonance are given.
Reviewer: V.C.Boffi

MSC:
34B05 Linear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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References:
[1] A. R. Aftabizadeh, Existence and uniqueness theorems for fourth-order boundary value problems, J. Math. Anal. Appl. 116 (1986), no. 2, 415 – 426. · Zbl 0634.34009
[2] Melvin S. Berger, Nonlinearity and functional analysis, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. Lectures on nonlinear problems in mathematical analysis; Pure and Applied Mathematics. · Zbl 0368.47001
[3] J. T. Schwartz, Nonlinear functional analysis, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher; Notes on Mathematics and its Applications. · Zbl 0203.14501
[4] Riaz A. Usmani, A uniqueness theorem for a boundary value problem, Proc. Amer. Math. Soc. 77 (1979), no. 3, 329 – 335. · Zbl 0424.34019
[5] Private communication with R. A. Usmani.
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