On the existence of solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces

Bogdan Rzepecki

Rendiconti del Seminario Matematico della Università di Padova (1986)

  • Volume: 76, page 201-206
  • ISSN: 0041-8994

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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 76 (1986): 201-206. <http://eudml.org/doc/108041>.

@article{Rzepecki1986,
author = {Rzepecki, Bogdan},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {existence; Darboux problem; Banach space; measure of noncompactness; Lipschitz condition},
language = {eng},
pages = {201-206},
publisher = {Seminario Matematico of the University of Padua},
title = {On the existence of solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces},
url = {http://eudml.org/doc/108041},
volume = {76},
year = {1986},
}

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
PB - Seminario Matematico of the University of Padua
VL - 76
SP - 201
EP - 206
LA - eng
KW - existence; Darboux problem; Banach space; measure of noncompactness; Lipschitz condition
UR - http://eudml.org/doc/108041
ER -

References

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  1. [1] S. Abian - A.B. Brown, On the solution of simultaneous first order implicit differential equations, Math. Annalen, 137 (1959), pp. 9-16. Zbl0088.29201MR104005
  2. [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. Zbl0174.46001MR222426
  3. [3] J. Banas - K. Goebel, Measures of Noncompactness in Banach Spaces, Lect. Notes Pure Applied Math., 60, Marcel Dekker, New York, 1980. Zbl0441.47056MR591679
  4. [4] R. Conti, Sulla risoluzione dell'equazione F(t, x, dx/dt) = 0, Annali di Mat. Pura ed Appl., 48 (1959), pp. 97-102. Zbl0092.07704MR110838
  5. [5] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova, 24 (1955), pp. 84-92. Zbl0064.35704MR70164
  6. [6] K. Deimling, Ordinary Differential Equations in Banach Spaces, Lect. Notes in Math., 596, Springer-Verlag, Berlin, 1977. Zbl0361.34050MR463601
  7. [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. Zbl0202.10003MR269957
  8. [8] R.H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, John Wiley and Sons, New York, 1976. Zbl0333.47023MR492671
  9. [9] P. Negrini, Sul problema di Darboux negli spazi di Banach, Bollettino U.M.I., (5), 17-A (1980), pp. 156-160. Zbl0545.35071
  10. [10] G. Pulvirenti, Equazioni differenziali in forma implicita in uno spazio di Banach, Annali di Mat. Pura ed Appl., 56 (1961), pp. 177-191. Zbl0106.09701MR133553
  11. [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. Zbl0435.47057MR560183
  12. [12] B.N. Sadovskii, Limit compact and condensing operators, Russian Math. Surveys, 27 (1972), pp. 86-144. Zbl0243.47033MR428132

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