Peano Type Theorem for Abstract Parabolic Equations
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 4, p. 1407-1421
@article{AIHPC_2009__26_4_1407_0,
     author = {Zubelevich, Oleg},
     title = {Peano Type Theorem for Abstract Parabolic Equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {26},
     number = {4},
     year = {2009},
     pages = {1407-1421},
     doi = {10.1016/j.anihpc.2008.12.002},
     zbl = {1172.35439},
     mrnumber = {2542731},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2009__26_4_1407_0}
}
Zubelevich, Oleg. Peano Type Theorem for Abstract Parabolic Equations. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 4, pp. 1407-1421. doi : 10.1016/j.anihpc.2008.12.002. http://www.numdam.org/item/AIHPC_2009__26_4_1407_0/

[1] Adams R. A., Sobolev Spaces, Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030

[2] Amann H., On Abstract Parabolic Fundamental Solutions, J. Math. Soc. Japan 39 (1987) 93-116. | MR 867989 | Zbl 0616.47032

[3] Amann H., Nonhomogeneous Linear and Quasilinear Elliptic and Parabolic Boundary Value Problems, in: Schmeisser H., Triebel H. (Eds.), Function Spaces, Differential Operators and Nonlinear Analysis, Teubner Texte zur Mathematik, vol. 133, Teubner, 1993, pp. 9-126, MR 94m:35153. | MR 1242579 | Zbl 0810.35037

[4] Amann H., Linear and Quasilinear Parabolic Problems. Abstract Linear Theory, Birkhäuser Verlag, 1995. | MR 1345385 | Zbl 0819.35001

[5] Arrieta J. M., Carvalho A. N., Abstract Parabolic Problems With Critical Nonlinearities and Applications to Navier-Stokes and Heat Equations, Trans. Amer. Math. Soc. 352 (1) (2000) 285-310. | MR 1694278 | Zbl 0940.35119

[6] Browder F. E., A New Generalization of the Schauder Fixed Point Theorem, Math. Ann. 174 (1967) 285-290. | MR 223944 | Zbl 0176.45203

[7] A.N. Carvalho, Abstract parabolic problems in ordered Banach spaces, Cadernos de Mathematica 02, 141-146, March 2001, Artigo Numero SMA No. 104.

[8] Diedonné J., Deux Exeples Singuliers D'équations Différentielles, Acta Sci. Math. (Szeged) 12 (1950) B 38-40. | MR 35397 | Zbl 0037.06002

[9] Dunford N., Schwartz J. T., Linear Operators. Part 1: General Theory, Interscience Publishers, New York, London, 1958. | MR 117523 | Zbl 0084.10402

[10] Dunford N., Schwartz J. T., Linear Operators. Part 3: Spectral Operators, Wiley-Interscience, New York, London, 1971. | Zbl 0243.47001

[11] Folland G., Real Analysis: Modern Techniques and Their Applications, second ed., Wiley-Interscience, 1999. | MR 1681462 | Zbl 0924.28001

[12] Frisch U., Turbulence. the Legacy of a.N. Kolmogorov, Cambridge University Press, 1995. | MR 1428905 | Zbl 0832.76001

[13] Fujita H., Kato T., On the Navier-Stokes Initial Value Problem I, Arch. Ration. Mech. Anal. 16 (1964) 269-315, MR 29:3774. | MR 166499 | Zbl 0126.42301

[14] Godunov A., Peano's Theorem in Banach Spaces, Funct. Anal. Appl. 9 (1975) 53-55. | MR 364797 | Zbl 0314.34059

[15] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981, MR 83j:35084. | MR 610244 | Zbl 0456.35001

[16] Kato T., Fujita H., On the Nonstationary Navier-Stokes System, Rend. Sem. Math. Univ. Padova 32 (1962) 243-260, MR 26:495. | Numdam | MR 142928 | Zbl 0114.05002

[17] Schwartz L., Analyse Mathématique, Hermann, 1967. | Zbl 0171.01301

[18] Yorke J., A Continuous Differential Equation in Hilbert Space Without Existence, Funkcial. Ekvac. 13 (1970) 19-21. | MR 264196 | Zbl 0248.34061