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. 
@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},
     pages = {201--206},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {76},
     year = {1986},
     mrnumber = {881570},
     zbl = {0656.35087},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_1986__76__201_0/}
}
TY  - JOUR
AU  - Rzepecki, Bogdan
TI  - On the existence of solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 1986
SP  - 201
EP  - 206
VL  - 76
PB  - Seminario Matematico of the University of Padua
UR  - http://archive.numdam.org/item/RSMUP_1986__76__201_0/
LA  - en
ID  - RSMUP_1986__76__201_0
ER  - 
%0 Journal Article
%A Rzepecki, Bogdan
%T On the existence of solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces
%J Rendiconti del Seminario Matematico della Università di Padova
%D 1986
%P 201-206
%V 76
%I Seminario Matematico of the University of Padua
%U http://archive.numdam.org/item/RSMUP_1986__76__201_0/
%G en
%F 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://archive.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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

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