First-order partial differential equations and consumer theory

Yuhki Hosoya

doi:10.3934/dcdss.2018065

Article Contents

2018, Volume 11, Issue 6: 1143-1167. Doi: 10.3934/dcdss.2018065

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First-order partial differential equations and consumer theory

Yuhki Hosoya

1-50-1601 Miyamachi, Fuchu, Tokyo, 183-0023, Japan

Received: January 31, 2017

Revised: May 31, 2017

Published: December 2018

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Abstract

In this paper, we show that the existence of a global solution of a standard first-order partial differential equation can be reduced to the extendability of the solution of the corresponding ordinary differential equation under the differentiable and locally Lipschitz environments. By using this result, we can produce many known existence theorems for partial differential equations. Moreover, we demonstrate that such a result can be applied to the integrability problem in consumer theory. This result holds even if the differentiability condition is dropped.

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Mathematics Subject Classification: Primary: 35A01, 91B08; Secondary: 91B16, 91B42.

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