Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 50, pp. 1-6.

Title: Generalized frameworks for first-order evolution inclusions
       based on Yosida approximations
       
Author: Ram U. Verma (Texas A&M Univ., Kingsville, TX, USA)

Abstract:
 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.