Accretive Nonlinear Operators in Banach Spaces
This chapter is concerned with the general theory of nonlinear quasi-m-accretive operators in Banach spaces with applications to the existence theory of nonlinear elliptic boundary value problems in L p -spaces and first-order quasilinear equations. While the monotone operators are defined in a duality pair (X;X*) and, therefore, in a variational framework, the accretive operators are intrinsically related to geometric properties of the space X and are more suitable for nonvariational and nonHilbertian existence theory of nonlinear problems. The presentation is confined, however, to the essential results of this theory necessary to the construction of accretive dynamics in the next chapter.
KeywordsBanach Space Monotone Operator Maximal Monotone Partial Differential Operator Topological Degree
Unable to display preview. Download preview PDF.
- 8.K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1975.Google Scholar
- 9.J. Dautray, J.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, Berlin, 1982.Google Scholar
- 10.T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Nonlinear Functional Analysis, F. Browder (Ed.), American Mathemathical Society, Providence, RI, 1970, pp. 138–161.Google Scholar
- 12.G. Stampacchia, Equations Elliptiques du Second Ordre à Coefficients Discontinues, Les Presses de l'Université de Montréal, Montréal, 1966.Google Scholar