ABSTRACT
By a first order multiplicative partial differential equation (MPDE) in n independent multiplicative variables https://www.w3.org/1998/Math/MathML"> x 1 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003394549/118beda6-6072-41d1-b22c-b02635a37673/content/math6_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> … , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003394549/118beda6-6072-41d1-b22c-b02635a37673/content/math6_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> x n , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003394549/118beda6-6072-41d1-b22c-b02635a37673/content/math6_3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> we mean any equation of the form https://www.w3.org/1998/Math/MathML"> F ( x 1 , … , x n , u , u x 1 * , … , u x n * ) = 0 * . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003394549/118beda6-6072-41d1-b22c-b02635a37673/content/math6_4.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
