Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 85, pp. 1-16.

Title: Generalized first-order nonlinear evolution equations and
       generalized  Yosida approximations based on
       H-maximal monotonicity frameworks

Author: Ram U. Verma (Florida Institute of Technology, Melbourne, FL, USA)

Abstract:
 First a general framework for the Yosida approximation is introduced
 based on the relative H-maximal monotonicity model, and then it is
 applied to the solvability of a general class of first-order nonlinear
 evolution equations. The obtained results generalize and unify a wide
 range of results to the context of the solvability of first-order
 nonlinear evolution equations in several settings.
 
Submitted June 5, 2009. Published July 10, 2009.
Math Subject Classifications: 49J40, 65B05.
Key Words: Generalized first-order evolution equations; variational problems; 
     maximal monotone mapping;  relative H-maximal monotone mapping; 
     relative H-maximal accretive mapping; generalized resolvent operator;
     general Yosida approximations