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, Volume 76  (1986), p. 201-206
@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},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {76},
     year = {1986},
     pages = {201-206},
     zbl = {0656.35087},
     mrnumber = {881570},
     language = {en},
     url = {http://www.numdam.org/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, Volume 76 (1986) , pp. 201-206. http://www.numdam.org/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