On First-Order Partial Differential Equations: An Existence Theorem and Its Applications

Research Article
Part of the Advances in Mathematical Economics book series (MATHECON, volume 20)


In this paper, we present an equivalence theorem between the existence of a global solution of a standard first-order partial differential equation and the extendability of the solution of corresponding ordinary differential equation. Moreover, we use this result to produce existence theorems on partial differential equation, and apply this theorem to the integrability problem in consumer theory.


Partial differential equation Global solution Nikliborc’s theorem Shephard’s lemma Expenditure function Integrability 


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Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of EconomicsKanto-Gakuin UniversityTokyoJapan

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