Non-compact perturbations of $m$-accretive operators in general Banach spaces
Cichoń, Mieczysław
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 403-409 / Harvested from Czech Digital Mathematics Library
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In this paper we deal with the Cauchy problem for differential inclusions governed by $m$-accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem $x'(t)\in -A x(t)+f(t,x(t))$, $x(0)=x_0$, where $A$ is an $m$-accretive operator, and $f$ is a continuous, but non-compact perturbation, satisfying some additional conditions.

Publié le : 1992-01-01
Classification:  34A60,  34G20,  47H06,  47H09,  47H20,  47N20,  58D25 
@article{118509,
     author = {Mieczys\l aw Cicho\'n},
     title = {Non-compact perturbations of $m$-accretive operators in general Banach spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {403-409},
     zbl = {0770.58003},
     mrnumber = {1209283},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118509}
}

Cichoń, Mieczysław. Non-compact perturbations of $m$-accretive operators in general Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 403-409. http://gdmltest.u-ga.fr/item/118509/

Banaś J.; Goebel K. Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Math. 60, Marcel Dekker, New York-Basel, 1980. | MR 0591679

Barbu V. Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden, 1976. | MR 0390843 | Zbl 0328.47035

Cellina A.; Marchi V. Non-convex perturbations of maximal monotone differential inclusions, Israel J. Math. 46 (1983), 1-11. (1983) | MR 0727019 | Zbl 0542.47036

Cichoń M. Multivalued perturbations of $m$-accretive differential inclusions in non-separable Banach spaces, Commentationes Math. 32, to appear. | MR 1384855

Colombo G.; Fonda A.; Ornelas A. Lower semicontinuous perturbations of maximal monotone differential inclusions, Israel J. Math. 61 (1988), 211-218. (1988) | MR 0941237 | Zbl 0661.47038

Daneš J. Generalized concentrative mappings and their fixed points, Comment. Math. Univ. Carolinae 11 (1970), 115-136. (1970) | MR 0263063

Goncharov V.V.; Tolstonogov A.A. Mutual continuous selections of multifunctions with non-convex values and its applications, Math. Sb. 182 (1991), 946-969. (1991) | MR 1128253

Gutman S. Evolutions governed by $m$-accretive plus compact operators, Nonlinear Anal. Th. Math. Appl. 7 (1983), 707-717. (1983) | MR 0707079 | Zbl 0518.34055

Gutman S. Existence theorems for nonlinear evolution equations, ibid. 11 (1987), 1193-1206. (1987) | MR 0913678 | Zbl 0642.47055

Martin R.H., Jr. Nonlinear Operators and Differential Equations in Banach Spaces, John Wiley, New York-London-Sydney-Toronto, 1976. | MR 0492671 | Zbl 0333.47023

Mitidieri E.; Vrabie I.I. Differential inclusions governed by non convex perturbations of $m$-accretive operators, Differential Integral Equations 2 (1989), 525-531. (1989) | MR 0996758 | Zbl 0736.34014

Schechter E. Evolution generated by semilinear dissipative plus compact operators, Trans. Amer. Math. Soc. 275 (1983), 297-308. (1983) | MR 0678351 | Zbl 0516.34061

Vrabie I.I. Compactness Methods for Nonlinear Evolutions, Pitman Monographs and Surveys in Pure and Applied Mathematics 32, Longman, Boston-London-Melbourne, 1987. | MR 0932730 | Zbl 0842.47040