An existence theorem for implicit differential equations in a Banach space

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In this paper it is proved an existence theorem for the implicit differential equation F(t, x, x′)=0; x(t0)=x0 on a Banach space where it is supposed that F satisfies certain Lipschitz condition in x′ and is α-Lipschitz or α-Lipschitz in x.


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Entrata in Redazione il 25 maggio 1977.

This research was done while the authors was visiting at the University of Minnesota.

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Benavides, T.D. An existence theorem for implicit differential equations in a Banach space. Annali di Matematica 118, 119–130 (1978).

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  • Differential Equation
  • Banach Space
  • Existence Theorem
  • Lipschitz Condition
  • Implicit Differential Equation