A singular Gierer-Meinhardt system of elliptic equations
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 4, pp. 503-522. 
@article{AIHPC_2000__17_4_503_0,
     author = {Choi, Y. S. and McKenna, P. J.},
     title = {A singular {Gierer-Meinhardt} system of elliptic equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {503--522},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {4},
     year = {2000},
     zbl = {0969.35062},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_2000__17_4_503_0/}
}
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Choi, Y. S.; McKenna, P. J. A singular Gierer-Meinhardt system of elliptic equations. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 4, pp. 503-522. http://archive.numdam.org/item/AIHPC_2000__17_4_503_0/

[1] Canic S., Lee Keyfitz B., An elliptic problem arising form the unsteady transonic small disturbance equation, J. Differential Equations 125 (1996) 548-574. | MR | Zbl

[2] Choi Y.S., Kim E.H., On the existence of positive solutions of quasilinear elliptic boundary value problems, J. Differential Equations 155 (1999) 423-442. | MR | Zbl

[3] Choi Y.S., Lazer A.C., Mckenna P.J., On a singular quasilinear anisotropic elliptic boundary value problem, Trans. Amer. Math. Soc. 347 (1995) 2633-2641. | MR | Zbl

[4] Choi Y.S., Mckenna P.J., On a singular quasilinear anisotropic elliptic boundary value problem, II, Trans. Amer. Math. Soc. 350 (1998) 2925-2937. | MR | Zbl

[5] Crandall M.G., Rabinowitz P.H., Tartar L., On a Dirichlet problem with a singular nonlinearity, Comm. PDE 2 (2) (1997) 193-222. | MR | Zbl

[6] Del Pino M.A., Radially symmetric layers in a semilinear elliptic system, Trans. Amer. Math. Soc. 347 (1995) 4807-4837. | MR | Zbl

[7] Gui C., Multipeak solutions for a semilinear Neumann problem, Duke Math. J. 84 ( 1996) 739-769. | MR | Zbl

[8] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, 1983. | MR | Zbl

[9] Lazer A.C., Mckenna P.J., On a singular nonlinear elliptic boundary value problem, Proc. Amer. Math. Soc. 111 (1991) 721-730. | MR | Zbl

[10] Ladyzenskaja O.A., Solonnikov V.A., Ural'Ceva N.N., Linear and Quasilinear Equations of Parabolic Type, Translation of Mathematical Monographs, Vol. 23, MS, 1968. | MR | Zbl

[11] Nachman A., Callegari A., A nonlinear singular boundary value problem in the theory of pseudoplastic fluids, SIAM J. Appl. Math. 28 (5) (1996) 271-281. | Zbl

[12] Ni W.-M., Takagi I., On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem: intermediate solutions, Duke Math. J. 94 (1998) 597-618. | MR | Zbl

[13] Ni W.-M., Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc. 45 (1998) 9-18. | MR | Zbl

[14] Protter M., Weinberger H., Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1984. | MR | Zbl

[15] Reichel W., Uniqueness for degenerate elliptic equations via Serrin's sweeping principle, General Inequalities 7, International Series of Numerical Mathematics, Birkhauser, Basel (to appear). | MR | Zbl

[16] Sattinger D.H., Topics in Stability and Bifurcation Theory, Lecture Notes in Mathematics, Vol. 309, Springer-Verlag, 1973. | MR | Zbl

[17] Serrin J., Zou H., Existence of positive entire solutions of elliptic Hamiltonian systems, Comm. Partial Differential Equations 23 (1998) 577-599. | MR | Zbl

[18] Lair A., Wood A., Existence of entire solutions of semilinear elliptic systems, Preprint. | Zbl

[19] Stuart C.A., Existence theorems for a class of nonlinear integral equations, Math. Z. 137 (1974) 49-66. | EuDML | MR | Zbl

[20] Taliaferro S.D., A nonlinear singular boundary value problem, Nonlinear Analysis TMA 3 (1979) 897-904. | MR | Zbl

[21] Turchin P., Reeve J.D., Cronin J.T., Spatial pattern formation in ecological systems: bridging theoretical and empirical approaches, in: Bascompte J., Sole R.V. (Eds.), Modelling Spatiotemporal Dynamics in Ecology, Pitman, 1997, pp. 195-210.