Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations
Marcus, M. ; Véron, L.
Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997), p. 237-274 / Harvested from Numdam
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@article{AIHPC_1997__14_2_237_0,
     author = {Marcus, M. and Veron, Laurent},
     title = {Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {14},
     year = {1997},
     pages = {237-274},
     mrnumber = {1441394},
     zbl = {0877.35042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1997__14_2_237_0}
}

Marcus, M.; Véron, L. Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) pp. 237-274. http://gdmltest.u-ga.fr/item/AIHPC_1997__14_2_237_0/

[BBL] R. Benguria, H. Brezis and E. Lies, The Thomas-Fermi-Von Weizsaäcker theory of atoms and molecules, Comm. Math. Phys., Vol. 79, 1981, pp. 167-180. | MR 612246 | Zbl 0478.49035

[BM1] C. Bandle and M. Marcus, Sur les solutions maximales de problèmes elliptiques non linéaires, C. R. Acad. Sci. Paris, 311, Ser. I, 1990, pp. 91-93. | MR 1065436 | Zbl 0726.35041

[BM2] C. Bandle and M. Marcus, Large solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behavior, Jl. d'Analyse Math., Vol. 58, 1992, pp. 9-24. | MR 1226934 | Zbl 0802.35038

[BM3] C. Bandle and M. Marcus, Large solutions of semilinear elliptic equations with singular coefficients, in Optimization and Nonlinear Analysis (ed. IOFFE, MARCUS, REICH), Pitman R. N. Series, Vol. 244, 1992, pp. 25-38. | MR 1184629 | Zbl 0795.35023

[BM4] C. Bandle and M. Marcus, Asymptotic behavior of solutions and their derivatives for semilinear elliptic problems with blowup on the boundary, Ann. Inst. Poincaré (to appear). | Numdam | MR 1326666 | Zbl 0840.35033

[BV] Brezis and L. Veron, Remouvable singularities for some nonlinear elliptic equations, Arch. Rat. Mech. Anal., Vol. 75, 1980, pp. 1-6. | MR 592099 | Zbl 0459.35032

[GNN] B. Gidas, W. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys., Vol. 68, 1979, pp. 209-243. | MR 544879 | Zbl 0425.35020

[K] J.B. Keller, On solutions of Δu = f(u), Comm. Pure Appl. Math., Vol. 10, 1957, pp. 503-510. | MR 91407 | Zbl 0090.31801

[LP] J.N. Lee and T.H. Parker, The Yamabe problem, Bull. Amer. Math. Soc., Vol. 17, 1987, pp. 37-91. | MR 888880 | Zbl 0633.53062

[LG] J.F. Le Gall, A path-valued Markov process and its connections with partial differential equations, Proc. 1st European Congress of Mathematics, Birkhäuser (to appear). | MR 1341844 | Zbl 0812.60058

[M] M. Marcus, On solutions with blow up at the boundary for a class of semilinear elliptic equations, in Developments in P.D.E. and Applications to Mathematical Physiscs, BUTTAZZO, GALDI and ZANGHIRATI ed., Plenum Press, 1993, pp. 65-77. | MR 1213924 | Zbl 0925.35066

[MV] M. Marcus and L. Veron, Uniqueness of solutions with blow up at the boundary for a class of nonlinear elliptic equations, C. R. Acad. Sci. Paris, 317, Ser. I, 1993, pp. 559-563. | MR 1240799 | Zbl 0803.35041

[O] R. Osserman, On the inequality Δu = f(u), Pacific Jl. Math., Vol. 7, 1957, pp. 1641-1647. | MR 98239 | Zbl 0083.09402

[Pr] Y. Pinchover, Criticality and ground states for second order elliptic equations, Jl. Diff. Equ., Vol. 80, 1989, pp. 237-250. | MR 1011149 | Zbl 0697.35036

[Py] R. Pinsky, Positive Harmonic Functions and Diffusion, Cambridge Studies in Advanced Math., Vol. 45, 1995. | MR 1326606 | Zbl 0858.31001

[V1] L. Veron, Semilinear elliptic equations with uniform blow up on the boundary, Jl. d'Analyse Math., Vol. 59, 1992, pp.231-250. | MR 1226963 | Zbl 0802.35042

[V2] L. Veron, Comportement asymptotique des solutions d'équations elliptiques semi linéaires dans RN, Ann. Mat. Pura Appl., Vol. 127, 1981, pp. 25-50. | MR 633393 | Zbl 0467.35013

[V3] L. Veron, Singular solutions of some nonlinear elliptic equations, Nonlinear Anal. T. M. & A.5, 1981, pp. 225-242. | Zbl 0457.35031