Gevrey theory for singular first-order partial differential equations in complex domains

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We studied first-order partial differential equations with singular points. Firstly, we gave conditions which ensure the existence and the uniqueness of formal power series solutions centered at the singular point, in forms of those for eigenvalues of some matrix determined by equations. Moreover, we gave conditions which assure the convergence of the formal solution. Secondly, we considered the linear equations called of nilpotent type, whose formal solution diverges, and we gave conditions under which the divergent solution is summable, in forms of global conditions (analytic continuation property, growth conditions or decreasing conditions) for coefficients of equations.