A Sturmian theorem for first order partial differential equations

Wong, Pui Kei

doi:10.1090/S0002-9947-1972-0294911-5

A Sturmian theorem for first order partial differential equations
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Trans. Amer. Math. Soc. 166 (1972), 125-131 Request permission

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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