Etude de quelques problèmes d'existence globale concernant l'équation(frac{{partial ^{r + s} u}}{{partial x^r partial y^s }} = fleft( {x,y,u,frac{{partial u}}{{partial x}},frac{{partial u}}{{partial y}},...,frac{{partial ^{p + q} u}}{{partial x^p partial y^q }},...} ight)left{ egin{gathered} 0 leqslant p leqslant r \ 0 leqslant q leqslant s \ p + q< r + s \ end{gathered} ight.)

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