Geodesic
Existence of solutions of perturbed O.D.E.'s in Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 3, pp. 463-470 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We consider a perturbed Cauchy problem like the following $$ {\hbox{\rm (PCP)}} \cases x' = A(t,x) +B(t,x) \ x(0)=x_0 \endcases $$ and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).
We consider a perturbed Cauchy problem like the following $$ {\hbox{\rm (PCP)}} \cases x' = A(t,x) +B(t,x) \ x(0)=x_0 \endcases $$ and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).
Classification : 34A12, 34G05, 34G20, 47H15, 47N20
Keywords: perturbed Cauchy problem; semi-inner product; measure of noncompactness 
@article{CMUC_1991_32_3_a7,
     author = {Emmanuele, Giovanni},
     title = {Existence of solutions of perturbed {O.D.E.'s} in {Banach} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {463--470},
     year = {1991},
     volume = {32},
     number = {3},
     mrnumber = {1159794},
     zbl = {0765.34044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1991_32_3_a7/}
}
TY  - JOUR
AU  - Emmanuele, Giovanni
TI  - Existence of solutions of perturbed O.D.E.'s in Banach spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1991
SP  - 463
EP  - 470
VL  - 32
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMUC_1991_32_3_a7/
LA  - en
ID  - CMUC_1991_32_3_a7
ER  - 
%0 Journal Article
%A Emmanuele, Giovanni
%T Existence of solutions of perturbed O.D.E.'s in Banach spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 1991
%P 463-470
%V 32
%N 3
%U http://geodesic.mathdoc.fr/item/CMUC_1991_32_3_a7/
%G en
%F CMUC_1991_32_3_a7
Emmanuele, Giovanni. Existence of solutions of perturbed O.D.E.'s in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 3, pp. 463-470. http://geodesic.mathdoc.fr/item/CMUC_1991_32_3_a7/

[1] Ambrosetti: Un teorema di esistenza per le equazioni differenziali negli spazi di Banach. Rend. Sem. Univ. Padova 39 (1967), 349-360. | MR

[2] Crandall M., Pazy A.: Nonlinear equations in Banach spaces. Israel J. Math. 11 (1972), 87-94. | MR

[3] Deimling K.: Ordinary Differential Equations in Banach Spaces. Lecture Notes in Math. 596, Springer Verlag 1977. | MR | Zbl

[4] Deimling K.: Open Problems for Ordinary Differential Equations in B-Spaces. Proceeding Equa-Diff. 1978, 127-137. | MR

[5] Diestel J., Uhl J.J., jr.: Vector Measures. Amer. Math. Soc. 1977. | MR | Zbl

[6] Dinculeanu N.: Vector Measures. Pergamon Press 1967. | MR | Zbl

[7] Dunford N., Schwartz J.T.: Linear Operators. part I, Interscience 1957. | Zbl

[8] Emmanuele G.: On a theorem of R.H. Martin on certain Cauchy problems for ordinary differential equations. Proc. Japan Acad. 61 (1985), 207-210. | MR | Zbl

[9] Emmanuele G.: Existence of approximate solutions for O.D.E.'s under Carathéodory assumptions in closed, convex sets of Banach spaces. Funkcialaj Ekvacioj, to appear.

[10] Evans L.C.: Nonlinear evolution equations in an arbitrary Banach space. Israel J. Math. 26 (1977), 1-42. | MR | Zbl

[11] Hu Shou Chuan: Ordinary differential equations involving perturbations in Banach spaces. J. Nonlinear Analysis, TMA 7 (1983), 933-940. | MR

[12] Kato T.: Nonlinear semigroups and evolution equations. J. Math. Soc. Japan 19 (1967), 508-520. | MR | Zbl

[13] Martin R.H.: Remarks on ordinary differential equations involving dissipative and compact operators. J. London Math. Soc. 10 (1975), 61-65. | MR | Zbl

[14] Martin R.H.: Nonlinear operators and differential equations in Banach spaces. Wiley and Sons 1976. | MR | Zbl

[15] Pierre M.: Enveloppe d'une famille de semi-groups dans un espace de Banach. C.R. Acad. Sci. Paris 284 (1977), 401-404. | MR

[16] Ricceri B., Villani A.: Separability and Scorza-Dragoni's property. Le Matematiche 37 (1982), 156-161. | MR

[17] Schechter E.: Evolution generated by continuous dissipative plus compact operators. Bull. London Math. Soc. 13 (1981), 303-308. | MR | Zbl

[18] Volkmann P.: Ein Existenzsatz für gewöhnliche differentialgleichungen in Banachräumen. Proc. Amer. Math. Soc. 80 (1980), 297-300. | MR | Zbl