A Sturmian theorem for first order partial differential equations

Author:
Pui Kei Wong

Journal:
Trans. Amer. Math. Soc. **166** (1972), 125-131

MSC:
Primary 35P05

MathSciNet review:
0294911

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Abstract | References | Similar Articles | Additional Information

Abstract: A pair of first order partial differential equations is considered. The system is transformed into a single nonlinear scalar equation of the Riccati type from which some Wirtinger type integral inequalities for functions of several variables are derived. A comparison theorem for two such pairs of first order equations is then proved using the Wirtinger inequalities.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0294911-5

Keywords:
Comparison theorems,
first order equations,
generalized Riccati equation,
Wirtinger inequalities

Article copyright:
© Copyright 1972
American Mathematical Society