Source type positive solutions of nonlinear parabolic inequalities

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1. [1] D.G. Aronson - J. Serrin, Local behaviour of solutions of quasilinear parabolic equations, Arch. Rat. Mech. Anal., 25 (1967), 81-122. Zbl0154.12001MR244638
2. [2] P. Aviles, Local behaviour of solutions of some elliptic equations, Comm. Math. Phys.108 (1987), 177-192. Zbl0617.35040MR875297
3. [3] P. Baras - J.C. Hassan - L. Veron, Compacité de l'opérateur définissant la solution d' une équation d'évolution non homogène, C.R. Acad. Sci. Paris t. 284 ser. A (1977), 799-802. Zbl0348.47026MR430864
4. [4] P. Baras - M. Pierre, Problèmes paraboliques semilinéaires avec données mesures, Appl. Anal. (1986). Zbl0582.35060
5. [5] P. Baras - M. Pierre, Critère d' existence de solutions positives pour des équations semi-linéaires non monotones, Ann. Inst. H. Poincaré, Anal. Non-linéaire2 (1985), 185-212. Zbl0599.35073MR797270
6. [6] H. Brezis - A. Friedman, Nonlinear parabolic equations involving measure as initial conditions, Jl. Math. Pures & Appl.62 (1983), 73-97. Zbl0527.35043MR700049
7. [7] H. Brezis - P.L. Lions, A note on isolated singularities for linear elliptic equations, Mathematical Analysis & Applications7A (1981), 263-266. Zbl0468.35036MR634242
8. [8] H. Brezis - L.A. Peletier - D. Terman, A very singular solution of the heat equation with absorption, Arch. Rat. Mech. Anal.95 (1986), 185-209. Zbl0627.35046MR853963
9. [9] X.Y. Chen - H. Matano - L. Veron, Anisotropic singularities of nonlinear elliptic equations in R2, Jl. Funct. Anal., 83 (1989), 50-97. Zbl0687.35020MR993442
10. [10] B. Gidas - J. Spruck, Global and local behaviour of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math.34 (1980), 525-598. Zbl0465.35003MR615628
11. [11] Y. Giga - R.V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math.38 (1985), 297-319. Zbl0585.35051MR784476
12. [12] A. Haraux - F.B. Weissler, Non-uniqueness for a semilinear initial value problem, Ind. Univ. Math. J1. 31 (1982), 167-189. Zbl0465.35049MR648169
13. [13] S. Kamin - L.A. Peletier, Singular solutions of the heat equation with absorption, Proc. Amer. Math. Soc.95 (1985), 205-210. Zbl0607.35046MR801324
14. [14] S. Kamin - L. Veron, Existence and uniqueness of the very singular solution of the porous media equation with absorption, Jl. d'Analyse Math.51 (1988), 245-258. Zbl0673.35044MR963156
15. [15] O.A. Ladyzenskaja - V.A. Solonnikov - N.N. Ural'ceva, Linear and quasilinear equations of parabolic type, Vol. 23, Trans. of Math. Mon., A.M.S.Providence (1968). Zbl0174.15403MR241822
16. [16] P.L. Lions, Isolated singularities in semilinear problems, J. Diff. Equ.38 (1980), 441-450. Zbl0458.35033MR605060
17. [17] I. Moutoussamy, Symétries et singularités de solutions d' équations paraboliques semi-linéaires, Ph. D. Thesis, Université de Tours (1987). 
18. [18] I. Moutoussamy - L. Veron, Isolated singularities of a semilinear heat equation, in preparation. 
19. [19] L. Oswald, Isolated, positive singularities for a nonlinear heat equation, Houston Jl. Math. (to appear). Zbl0696.35023MR998457
20. [20] Y. Richard - L. Veron, Isotropic singularities of solutions of nonlinear elliptic inequalities, Ann. Inst. H. Poincaré, Anal. Nonlinéaire, 6 (1989), 37-72. Zbl0702.35083MR984147
21. [21] F.B. Weissler, Asymptotic analysis of an ordinary differential equation and non-uniqueness for a semilinear partial differential equation, Arch. Rat. Mech. Anal.91 (1986), 231-245. Zbl0614.35043MR806003
22. [22] F.B. Weissler, Rapidly decaying solutions of an ordinary differential equation with applications to semilinear elliptic and parabolic partial differential equations, Arch. Rat. Mech. Anal.91 (1986), 247-266. Zbl0604.34034MR806004