本稿は積分可能性問題の理論的な基礎を固めるために必要な偏微分方程式, および全微分方程式の解の存在定理について解説を行い, その導出を行う。主に行われるのは仮線形偏微分方程式の解の存在定理と, Frobeniusの定理の証明である。また, 積分可能性条件と需要関数の条件の対応関係についても議論する。
This study explains the existence theorem on a solution for partial differential equations necessary for solidifying the theoretical basis of integrability problems, as well as total differential equations, and performs its derivation. 
Primarily, an existence theorem on the solution of provisionally linear partial differential equations and a proof of the Frobenius theorem was performed. In addition, we discuss the correspondence of conditions for integrability and demand functions.

論説