Existence and attractivity results for a class of degenerate functional-parabolic problems
Rendiconti del Seminario Matematico della Università di Padova, Tome 78 (1987), pp. 109-124. 
@article{RSMUP_1987__78__109_0,
     author = {Badii, M. and Diaz, J. I. and Tesei, A.},
     title = {Existence and attractivity results for a class of degenerate functional-parabolic problems},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {109--124},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {78},
     year = {1987},
     mrnumber = {934509},
     zbl = {0669.35057},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1987__78__109_0/}
}
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Badii, M.; Diaz, J. I.; Tesei, A. Existence and attractivity results for a class of degenerate functional-parabolic problems. Rendiconti del Seminario Matematico della Università di Padova, Tome 78 (1987), pp. 109-124. http://www.numdam.org/item/RSMUP_1987__78__109_0/

[1] D.G. Aronson - M.G. Crandall - L.A. Peletier, Stabilization of solutions of a degenerate nonlinear diffusion problem, Nonlinear Anal. TMA, 6 (1982), pp. 1001-1022. | MR | Zbl

[2] P. Baras, Compacité de l'operateur f → u solution d'une equation non linéaire (du/dt) + Au = f, C. R. Acad. Sci. Paris, Sér. A, 286 (1978). pp. 1113-1116. | Zbl

[3] J. Bebernes - R. ELY, Existence and invariance for parabolic functional equations, Nonlinear Anal. TMA, 7 (1983), pp. 1225-1236. | MR | Zbl

[4] H. Brézis, New results concerning monotone operators and nonlinear semigroups, in « Analysis of nonlinear problems », pp. 2-27 (Research Institute for Mathematical Sciences, Kyoto University, 1974). | MR

[5] H. Brézis - A. FRIEDMAN, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl., 62 (1983), pp. 73-97. | MR | Zbl

[6] H. Brézis - W.A. Strauss, Semi-linear second-order elliptic equations in L1, J. Math. Soc. Japan, 25 (1973), pp. 565-590. | MR | Zbl

[7] P. De MOTTONI - A. SCHIAFFINO - A. TESEI, Attractivity properties of nonnegative solutions for a class of nonlinear degenerate parabolic problems, Ann. Mat. Pura Appl., 136 (1984), pp. 35-48. | MR | Zbl

[8] J.I. Diaz - J. Hernández, On the existence of a free boundary for a class of reaction-diffusion systems, SIAM J. Math. Anal., 15 (1984), pp. 670-685. | MR | Zbl

[9] H. Engler, Invariant sets for functional differential equations in Banach spaces and applications, Nonlinear Anal. TMA, 5 (1981), pp. 1225-1243. | MR | Zbl

[10] H. Engler, Functional differential equations in Banach spaces: growth and decay of solutions, J. für Reine u. Angew. Math., 322 (1981), pp. 53-73. | MR | Zbl

[11] M.E. Gurtin - R.C. Maccamy, On the diffusion of biological populations, Math. Biosci., 33 (1977), pp. 35-49. | MR | Zbl

[12] L.A. Peletier - A. Tesei, Global bifurcation and attractivity of stationary solutions of a degenerate diffusion equation, preprint (1985).

[13] V.P. Politjukov, On the theory of upper and lower solutions and the solvability of quasilinear integro-differential equations, Math. USSR Sbornik, 35 (1979), pp. 499-507. | MR | Zbl

[14] M.A. Pozio - A. Tesei, Support properties of solutions for a class of degenerate parabolic problems, preprint (1984). | MR

[15] M.A. Pozio - A. Tesei, Degenerate parabolic problems in population dynamics, Japan J. Appl. Math. (to appear). | MR

[16] M. Schatzman, Stationary solutions and asymptotic behaviour of a quasilinear degenerate parabolic equation, Indiana Univ. Math. J., 33 (1984), pp. 1-30. | MR | Zbl

[17] A. Schiaffino, On a diffusion Volterra equation, Nonlinear Anal. TMA, 3 (1979), pp. 595-600. | MR | Zbl

[18] A. Schiaffino - A. Tesei, Asymptotic stability properties for nonlinear diffusion Volterra equations, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 67 (1979), pp. 227-232. | MR | Zbl

[19] A. Schiaffino - A. Tesei, Monotone methods and attractivity results for Volterra integropartial differential equations, Proc. Royal Soc. Edinburgh, 89A (1981), pp. 135-142. | MR | Zbl

[20] J. Spruck, Uniqueness in a diffusion model of population biology, Comm. in Partial Differential Equations, 8 (1983), pp. 1605-1620. | MR | Zbl

[21] G. Stampacchia, On some regular multiple integral problems in the calculus of variations, Comm. Pure Appl. Math., 16 (1963), pp. 383-421. | MR | Zbl

[22] A. Tesei, Stability properties for partial Volterra integrodifferential equations, Ann. Mat. Pura Appl., 126 (1980), pp. 103-115. | MR | Zbl

[23] L. Tsai, On integro-differential equations of parabolic type, Bull. Inst. Math. Acad. Sinica, 9 (1981), pp. 311-320. | MR | Zbl

[24] V. Volterra, Leçons sur la théorie mathématique de la lutte pour la vie (Paris: Gauthier-Villars, 1931). | Zbl

[25] I.I. Vrabie, The nonlinear version of Pazy's local existence theorem, Israel J. Math., 32 (1979), pp. 221-235. | MR | Zbl

[26] I.I. Vrabie, Compactness methods for an abstract nonlinear Volterra integrodifferential equation, Nonlinear Analysis TMA, 5 (1981), pp . 355-371. | MR | Zbl

[27] I.I. Vrabie, An existence result for a class of nonlinear evolution equations in Banach spaces, Nonlinear Analysis TMA, 6 (1982), pp. 711-722. | MR | Zbl

[28] Y. Yamada, On a certain class of semilinear Volterra diffusion equations, J. Math. Anal. Appl., 88 (1982), pp. 433-451. | MR | Zbl