Geodesic
Existence of solutions of the Darboux problem for partial differential equations in Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 28 (1987) no. 3, pp. 421-426 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Classification : 34G20, 35A05, 35L15, 35L75, 47H10 
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Rzepecki, Bogdan. Existence of solutions of the Darboux problem for partial differential equations in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 28 (1987) no. 3, pp. 421-426. http://geodesic.mathdoc.fr/item/CMUC_1987_28_3_a2/

[1] A. AMBROSETTI: Un teorema di esistenza per le equazioni differenziali negli spazi di Banach. Rend. Sem. Mat. Univ. Padova 39 (1967), 349-360. | MR | Zbl

[2] J. BANAŚ K. GOEBEL: Measure of Noncompactness in Banach Spaces. Lect. Notes Pure Applied Math. 60, Marcel Dekker, New York 1980. | MR

[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

[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

[5] J. CONLAN: An existence theorem for the equation $u_xyz = f$. Arch. Rational Mech. Anal. 9 (1962), 64-76. | MR

[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

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

[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

[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

[10] R. D. NUSSBAUM: The fixed point index and fixed point theorems for k-set-contraction. Ph.D. dissertation, University of Chicago, 1969.

[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. | MR | Zbl

[12] B. N. SADOVSKII: Limit compact and condensing operators. Math. Surveys, 27 (1972), 86-144. | MR