# American Institute of Mathematical Sciences

December  2018, 11(6): 1143-1167. doi: 10.3934/dcdss.2018065

## First-order partial differential equations and consumer theory

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

Received  February 2017 Revised  June 2017 Published  June 2018

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.

Citation: Yuhki Hosoya. First-order partial differential equations and consumer theory. Discrete & Continuous Dynamical Systems - S, 2018, 11 (6) : 1143-1167. doi: 10.3934/dcdss.2018065
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