Electron. J. Diff. Eqns., Vol. 2000(2000), No. 34, pp. 1-20.

Non-degenerate implicit evolution inclusions

Kenneth Kuttler

Abstract:
We prove the existence of solutions for the implicit evolution inclusion
$$ ( B(t) u( t) ) ' + A(t,u(t)) \ni f(t) $$
under conditions that are easy to verify on the set valued operator $A( t,\cdot)$ and that do not imply the operator is monotone. We also present an example where our existence theorem applies to a time dependent implicit inclusion.

Submitted April 12, 2000. Published May 12, 2000.
Math Subject Classifications: 34A60, 35R70, 35A05, 34A09, 35K20, 47H15.
Key Words: Nonlinear evolution inclusion, pseudo-monotone mapping, implicit inclusions.

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Kenneth Kuttler
Department of Mathematics
Brigham Young University
Provo, Utah, 84602 USA
email: klkuttle@mail.math.byu.edu

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