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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:
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


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