Electron. J. Diff. Equ., Vol. 2011 (2011), No. 50, pp. 1-6.

Generalized frameworks for first-order evolution inclusions based on Yosida approximations

Ram U. Verma

First, general frameworks for the first-order evolution inclusions are developed based on the A-maximal relaxed monotonicity, and then using the Yosida approximation the solvability of a general class of first-order nonlinear evolution inclusions is investigated. The role the A-maximal relaxed monotonicity is significant in the sense that it not only empowers the first-order nonlinear evolution inclusions but also generalizes the existing Yosida approximations and its characterizations in the current literature.

Submitted December 25, 2010. Published April 11, 2011.
Math Subject Classifications: 49J40, 65B05.
Key Words: Generalized first-order evolution inclusions; variational problems; maximal monotone mapping; A-maximal relaxed monotone mapping; generalized resolvent operator; general Yosida approximations.

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Ram U. Verma
Texas A&M University, Department of Mathematics
Kingsville, TX 78363, USA
email: verma99@msn.com

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