On First-Order Partial Differential Equations: An Existence Theorem and Its Applications
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.
KeywordsPartial differential equation Global solution Nikliborc’s theorem Shephard’s lemma Expenditure function Integrability
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