| Title:
|
Existence of solutions of the Darboux problem for partial differential equations in Banach spaces (English) |
| Author:
|
Rzepecki, Bogdan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
28 |
| Issue:
|
3 |
| Year:
|
1987 |
| Pages:
|
421-426 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34G20 |
| MSC:
|
35A05 |
| MSC:
|
35L15 |
| MSC:
|
35L75 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 0638.35058 |
| idMR:
|
MR912570 |
| . |
| Date available:
|
2008-06-05T21:29:39Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106554 |
| . |
| Reference:
|
[1] A. AMBROSETTI: Un teorema di esistenza per le equazioni differenziali negli spazi di Banach.Rend. Sem. Mat. Univ. Padova 39 (1967), 349-360. Zbl 0174.46001, MR 0222426 |
| Reference:
|
[2] J. BANAŚ K. GOEBEL: Measure of Noncompactness in Banach Spaces.Lect. Notes Pure Applied Math. 60, Marcel Dekker, New York 1980. MR 0591679 |
| Reference:
|
[3] L. CASTELLANO: Sull' approssimazione, col metodo di Tonelli, delle soluzioni del problema di Darboux per l'equazione $u_{xyz} = f(x,y,z,u,u_x,u_y ,u_z)$.Le Matematiche 23 (1) (196B), 107-123. MR 0241830 |
| Reference:
|
[4] S. C. CHU J. B. DIAZ: The Coursat problem for the partial differential equation $u_xyz = f$.A mirage, J. Math. Mech. 16 (1967), 709-713. MR 0203264 |
| Reference:
|
[5] J. CONLAN: An existence theorem for the equation $u_xyz = f$.Arch. Rational Mech. Anal. 9 (1962), 64-76. MR 0132898 |
| Reference:
|
[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. MR 0361946 |
| Reference:
|
[7] K. DEIMLING: Ordinary Differential Equations in Banach Spaces.Lect. Notes in Math. 596, Springer-Verlag, Berlin 1977. Zbl 0361.34050, MR 0463601 |
| Reference:
|
[8] M. FRASCA: Su un problema ai limiti per l'equazione $u_{xyz} = f(x,y,z,u,u_x,u_y,u_z)$.Matematiche (Catania) 21 (1966), 396-412. MR 0209673 |
| Reference:
|
[9] M. KWAPISZ B. PALCZEWSKI W. PAWELSKI: Sur l'équations et l'unicité des solutions de certaines équations differentielles du type $u_{xyz} = f(x,y,z,u,u_x,u_y,u_z,u_{xy},u_{xz},u_{yz})$.Arm. Polon. Math. 11 (1961), 75-106. MR 0136880 |
| Reference:
|
[10] R. D. NUSSBAUM: The fixed point index and fixed point theorems for k-set-contraction.Ph.D. dissertation, University of Chicago, 1969. |
| Reference:
|
[11] B. PALCZEWSKI: Existence and uniqueness of solutions of the Darboux problem for the equation${\partial^3u}\over {\partial x_1 \partial x_2 \partial x_3} = f {(x_1, x_2, x_3, u, {{\partial u}\over{ \partial x_1}}, {{\partial u}\over{ \partial x_2}}, {{\partial u}\over{ \partial x_3}}, {{\partial^2 u}\over{ \partial x_1 \partial x_2}}, {{\partial^2 u}\over{ \partial x_1 \partial x_3}}, {{\partial^2 u}\over{ \partial x_2 \partial x_3}})}$.Ann. Polon. Math. 13 (1963), 267-277. Zbl 0168.07502, MR 0157135 |
| Reference:
|
[12] B. N. SADOVSKII: Limit compact and condensing operators.Math. Surveys, 27 (1972), 86-144. MR 0428132 |
| . |
