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The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations.

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Operators with regular singularities. One variable case - Operators with regular singularities. Several variables case - Formal and convergent solutions of singular partial differential equations - Local study of differential equations of the form xy´ f(x,y) near x 0 - Holomorphic and singular solutions of non linear singular first order partial differential equations - Maillet´s type theorems for non linear singular partial differential equations - Maillet´s type theorems for non linear singular partial differential equations without linear part - Holomorphic and singular solutions of non linear singular partial differential equations - On the existence of holomorphic solutions of the Cauchy problem for non linear partial differential equations - Maillet´s type theorems for non linear singular integro-differential equations.

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Prof. Raymond Gerard ist am Institut de Recherche Mathématique Alsacien an der Université Louis Pasteur in Strasbourg beschäftigt. Prof. Hidetoshi Tahara lehrt an der Sophia Universität in Tokyo.

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