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Singular solutions of nonlinear partial differential equations with resonances. (English) Zbl 1136.35008

Summary: We present a Frobenius type theorem for a system of nonlinear partial differential equations. Typical application is the normal form theory of a singular vector field. The construction of a singular solution is closely related with a Riemann-Hilbert factorization.

MSC:

35B34 Resonance in context of PDEs
35L40 First-order hyperbolic systems
35Q15 Riemann-Hilbert problems in context of PDEs
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