Perturbations of M-accretive operators and quasi-linear evolution equations

Athanassios G. KARTSATOS

doi:10.2969/jmsj/03010075

Athanassios G. KARTSATOS

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JOURNAL FREE ACCESS

1978 Volume 30 Issue 1 Pages 75-84

DOI https://doi.org/10.2969/jmsj/03010075

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Published: 1978 Received: June 29, 1976 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) C. Corduneanu, Sur les systèmes différentiels de la forme y'=A(x, y)y+b(x, y), An. Sti. Univ. “Al I. Cuza”. Iasi, (N. S) 4 (1958), 45-52.
2) C. Avramescu, Sur une équation non linéaire dans les espaces de Banach, Act. Conf. Intern. “Equa-Dill 73”. Bruxelles et Louvain-La-Neuve, (1973), 97-107.
3) K. Gröger, Zur Theorie von Evolutionsgleichungen, in den die “Vorgeschichte” eine Rolle spielt, Math. Nachr., 56 (1973), 63-72.
4) A. G. Kartsatos, Nonzero solutions to boundary value problems for nonlinear systems, Pacific J. Math., 52 (1974), 425-433.
5) A. G. Kartsatos, Bounded solutions to perturbed nonlinear systems and asymptotic relationships, J. Reine Angew. Math., 273 (1975), 170-177.
6) A. G. Kartsatos, Stability via Tychonov's theorem, Internat. J. Systems Sci., 5 (1974), 933-937.
7) A. G. Kartsatos, and J. R. Ward, Boundedness and existence of periodic solutions of quasi-linear systems, J. Inst. Math. Appl., 15 (1975), 187-194.
8) T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 503-520.
9) T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Proc. Symp. Pure Math., 18 (1970), 138-161.
10) T. Kato, Quasi-linear equations of evolution with applications to partial differential equations, Proc. Symp. Spectral Theory Differential Equations, Lecture Notes No. 448, Springer-Verlag, New York, 1975.
11) A. Lasota and Z. Opial, Sur les solutions periodiques des équations différentielles ordinaires, Ann. Polon. Math., 16 (1964), 69-94.
12) J. L. Massera and J. J. Schäffer, Linear differential equations and functional analysis, I., Ann. of Math., 67 (1958), 517-573.
13) J. L. Massera and J. J. Schäffer, Linear differential equations and functional analysis, IV, Math. Ann., 139 (1960), 287-342.
14) J. Mermin, Accretive operators and nonlinear semigroups, Doct. Dissert., University of California, Berkeley, 1968.
15) Z. Opial, Linear problems for systems of nonlinear differential equations, J. Differential Equations, 3 (1967), 580-594.
16) J. R. Ward, Existence of solutions to quasi-linear differential equations in a Banach space, to appear.

Right : [1] C. Corduneanu, Sur les systèmes différentiels de la forme y'=A(x,y)y+b(x,y), An. Sti. Univ. “Al I. Cuza”, Iasi, (N. S) 4 (1958), 45-52.
[2] C. Avramescu, Sur une équation non linéaire dans les espaces de Banach, Act. Conf. Intern. “Equa-Diff 73”, Bruxelles et Louvain-La-Neuve, (1973), 97-107.
[3] K. Gröger, Zur Theorie von Evolutionsgleichungen, in den die “Vorgeschichte” eine Rolle spielt, Math. Nachr., 56 (1973), 63-72.
[4] A. G. Kartsatos, Nonzero solutions to boundary value problems for nonlinear systems, Pacific J. Math., 52 (1974), 425-433.
[5] A. G. Kartsatos, Bounded solutions to perturbed nonlinear systems and asymptotic relationships, J. Reine Angew. Math., 273 (1975), 170-177.
[6] A. G. Kartsatos, Stability via Tychonov's theorem, Internat. J. Systems Sci., 5 (1974), 933-937.
[7] A. G. Kartsatos, and J. R. Ward, Boundedness and existence of periodic solutions of quasi-linear systems, J. Inst. Math. Appl., 15 (1975), 187-194.
[8] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 503-520.
[9] T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Proc. Symp. Pure Math., 18 (1970), 138-161.
[10] T. Kato, Quasi-linear equations of evolution with applications to partial differential equations, Proc. Symp. Spectral Theory Differential Equations, Lecture Notes No. 448, Springer-Verlag, New York, 1975.
[11] A. Lasota and Z. Opial, Sur les solutions periodiques des équations différentielles ordinaires, Ann. Polon. Math., 16 (1964), 69-94.
[12] J. L. Massera and J. J. Schäffer, Linear differential equations and functional analysis, I., Ann. of Math., 67 (1958), 517-573.
[13] J. L. Massera and J. J. Schäffer, Linear differential equations and functional analysis, IV, Math. Ann., 139 (1960), 287-342.
[14] J. Mermin, Accretive operators and nonlinear semigroups, Doct. Dissert., University of California, Berkeley, 1968.
[15] Z. Opial, Linear problems for systems of nonlinear differential equations, J. Differential Equations, 3 (1967), 580-594.
[16] J. R. Ward, Existence of solutions to quasi-linear differential equations in a Banach space, to appear.

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