On the existence of solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces
Rzepecki, Bogdan
Rendiconti del Seminario Matematico della Università di Padova, Tome 76 (1986), p. 201-206 / Harvested from Numdam
Publié le : 1986-01-01
@article{RSMUP_1986__76__201_0,
     author = {Rzepecki, Bogdan},
     title = {On the existence of solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {76},
     year = {1986},
     pages = {201-206},
     mrnumber = {881570},
     zbl = {0656.35087},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1986__76__201_0}
}
Rzepecki, Bogdan. On the existence of solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces. Rendiconti del Seminario Matematico della Università di Padova, Tome 76 (1986) pp. 201-206. http://gdmltest.u-ga.fr/item/RSMUP_1986__76__201_0/

[1] S. Abian - A.B. Brown, On the solution of simultaneous first order implicit differential equations, Math. Annalen, 137 (1959), pp. 9-16. | MR 104005 | Zbl 0088.29201

[2] A. Ambrosetti, Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Mat. Univ. Padova, 39 (1967), pp. 349-360. | Numdam | MR 222426 | Zbl 0174.46001

[3] J. Banas - K. Goebel, Measures of Noncompactness in Banach Spaces, Lect. Notes Pure Applied Math., 60, Marcel Dekker, New York, 1980. | MR 591679 | Zbl 0441.47056

[4] R. Conti, Sulla risoluzione dell'equazione F(t, x, dx/dt) = 0, Annali di Mat. Pura ed Appl., 48 (1959), pp. 97-102. | MR 110838 | Zbl 0092.07704

[5] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova, 24 (1955), pp. 84-92. | Numdam | MR 70164 | Zbl 0064.35704

[6] K. Deimling, Ordinary Differential Equations in Banach Spaces, Lect. Notes in Math., 596, Springer-Verlag, Berlin, 1977. | MR 463601 | Zbl 0361.34050

[7] K. Goebel - W. Rzymowski, An existence theorem for the equations x' = f (t, x) in Banach space, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys., 18 (1970), pp. 367-370. | MR 269957 | Zbl 0202.10003

[8] R.H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, John Wiley and Sons, New York, 1976. | MR 492671 | Zbl 0333.47023

[9] P. Negrini, Sul problema di Darboux negli spazi di Banach, Bollettino U.M.I., (5), 17-A (1980), pp. 156-160. | Zbl 0545.35071

[10] G. Pulvirenti, Equazioni differenziali in forma implicita in uno spazio di Banach, Annali di Mat. Pura ed Appl., 56 (1961), pp. 177-191. | MR 133553 | Zbl 0106.09701

[11] B. Rzepecki, Remarks on Schauder's fixed point principle and its applications, Bull. Acad. Polon. Sci., Sér. Sci. Math., 27 (1979), pp. 473-479. | MR 560183 | Zbl 0435.47057

[12] B.N. Sadovskii, Limit compact and condensing operators, Russian Math. Surveys, 27 (1972), pp. 86-144. | MR 428132 | Zbl 0243.47033