Electron. J. Diff. Eqns., Vol. 2009(2009), No. 85, pp. 1-16.

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

Ram U. Verma

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

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Ram U. Verma
Florida Institute of Technology
Department of Mathematical Sciences
Melbourne, FL 32901, USA
email: verma99@msn.com

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