The One-Dimensional Maximum Principle

Murray H. Protter and Hans F. Weinberger
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Murray H. Protter: University of California, Department of Mathematics
Hans F. Weinberger: University of Minnesota, Institute for Mathematics and its Applications

Chapter Chapter 1 in Maximum Principles in Differential Equations, 1984, pp 1-50 from Springer

Abstract: Abstract A function u(x) that is continuous on the closed interval* [a, b] takes on its maximum at a point on this interval. If u(x) has a continuous second derivative, and if u has a relative maximum at some point c between a and b, then we know from elementary calculus that (1) $$ u'(c) = 0\;and\;u''(c) \leqslant 0 $$ .

Keywords: Lower Bound; Maximum Principle; Interior Point; Comparison Theorem; Conjugate Point (search for similar items in EconPapers)
Date: 1984
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DOI: 10.1007/978-1-4612-5282-5_1

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