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Cauchy-Kovalevskaya theory for equations with deviating variables. (English) Zbl 0929.35004
Summary: We prove existence theorems of the Cauchy-Kovalevskaya type for linear partial differential equations with deviating variables. Our results generalize to strongly coupled systems and equations with deviations dependent on the unknown function. We give also sufficient conditions for a nontrivial case where the deviations depend on the unknown function.

MSC:
35A10 Cauchy-Kovalevskaya theorems
35R10 Functional partial differential equations
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35F10 Initial value problems for linear first-order PDEs
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