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Monotone techniques and some existence-uniqueness theorems for two point boundary value problems

Published online by Cambridge University Press:  14 November 2011

Song-Sun Lin
Song-Sun Lin
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsin-Chu, Taiwan 300, Republic of China
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Synopsis

In this paper we study the existence and uniqueness of the two point boundary value problems −(p(x)u′(x))′ = f(x, u(x), u′(x)), xε(0, 1), u′(0)−cu(0) = 0 = u′(1) + du(1), where ∂f/∂u is bounded. above by the least eigenvalue of associated linear problems and ∂f/∂u is bounded. By using monotone techniques to investigate the equivalent problem −(p(x)u′(x))′ + r(x)u(x) = f(x, u(x), u′(x)) + r(x)u(x) where r ε C[0, 1] we show that

gives the optimal bounds for ∂f/∂u and ∂f/u′ when c and d are nonnegative constants.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 3-4 , 1982 , pp. 265 - 275
Copyright
Copyright © Royal Society of Edinburgh 1982

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