Existence of solutions of the Darboux problem for partial differential equations in Banach spaces

Bogdan Rzepecki

Commentationes Mathematicae Universitatis Carolinae (1987)

  • Volume: 028, Issue: 3, page 421-426
  • ISSN: 0010-2628

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Rzepecki, Bogdan. "Existence of solutions of the Darboux problem for partial differential equations in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 028.3 (1987): 421-426. <http://eudml.org/doc/17556>.

@article{Rzepecki1987,
author = {Rzepecki, Bogdan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {third order; existence; Darboux problem; fixed point theorem; Banach space; regularity; measure of noncompactness},
language = {eng},
number = {3},
pages = {421-426},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Existence of solutions of the Darboux problem for partial differential equations in Banach spaces},
url = {http://eudml.org/doc/17556},
volume = {028},
year = {1987},
}

TY - JOUR
AU - Rzepecki, Bogdan
TI - Existence of solutions of the Darboux problem for partial differential equations in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1987
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 028
IS - 3
SP - 421
EP - 426
LA - eng
KW - third order; existence; Darboux problem; fixed point theorem; Banach space; regularity; measure of noncompactness
UR - http://eudml.org/doc/17556
ER -

References

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  1. A. AMBROSETTI, Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Mat. Univ. Padova 39 (1967), 349-360. (1967) Zbl0174.46001MR0222426
  2. J. BANAŚ K. GOEBEL, Measure of Noncompactness in Banach Spaces, Lect. Notes Pure Applied Math. 60, Marcel Dekker, New York 1980. (1980) MR0591679
  3. L. CASTELLANO, Sull’ approssimazione, col metodo di Tonelli, delle soluzioni del problema di Darboux per l’equazione u x y z = f ( x , y , z , u , u x , u y , u z ) , Le Matematiche 23 (1) (196B), 107-123. (196B) MR0241830
  4. S. C. CHU J. B. DIAZ, The Coursat problem for the partial differential equation u x y z = f , A mirage, J. Math. Mech. 16 (1967), 709-713. (1967) MR0203264
  5. J. CONLAN, An existence theorem for the equation u x y z = f , Arch. Rational Mech. Anal. 9 (1962), 64-76. (1962) MR0132898
  6. J. DANEŠ, On densifying and related mappings and their application in nonlinear functional analysis, Theory of Nonlinear Operators, Akademie-Verlag, Berlin 1974, 15-46. (1974) MR0361946
  7. K. DEIMLING, Ordinary Differential Equations in Banach Spaces, Lect. Notes in Math. 596, Springer-Verlag, Berlin 1977. (1977) Zbl0361.34050MR0463601
  8. M. FRASCA, Su un problema ai limiti per l’equazione u x y z = f ( x , y , z , u , u x , u y , u z ) , Matematiche (Catania) 21 (1966), 396-412. (1966) MR0209673
  9. M. KWAPISZ B. PALCZEWSKI W. PAWELSKI, Sur l’équations et l’unicité des solutions de certaines équations differentielles du type u x y z = f ( x , y , z , u , u x , u y , u z , u x y , u x z , u y z ) , Arm. Polon. Math. 11 (1961), 75-106. (1961) MR0136880
  10. R. D. NUSSBAUM, The fixed point index and fixed point theorems for k-set-contraction, Ph.D. dissertation, University of Chicago, 1969. (1969) 
  11. B. PALCZEWSKI, Existence and uniqueness of solutions of the Darboux problem for the equation ∂ 3 u ∂ x 1 ∂ x 2 ∂ x 3 = f ( x 1 , x 2 , x 3 , u , ∂ u ∂ x 1 , ∂ u ∂ x 2 , ∂ u ∂ x 3 , ∂ 2 u ∂ x 1 ∂ x 2 , ∂ 2 u ∂ x 1 ∂ x 3 , ∂ 2 u ∂ x 2 ∂ x 3 ) , Ann. Polon. Math. 13 (1963), 267-277. (1963) Zbl0168.07502MR0157135
  12. B. N. SADOVSKII, Limit compact and condensing operators, Math. Surveys, 27 (1972), 86-144. (1972) MR0428132

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