A singular Gierer—Meinhardt system of elliptic equations

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1. [1] Canic S., Lee Keyfitz B., An elliptic problem arising form the unsteady transonic small disturbance equation, J. Differential Equations125 (1996) 548-574. Zbl0869.35043MR1378766
2. [2] Choi Y.S., Kim E.H., On the existence of positive solutions of quasilinear elliptic boundary value problems, J. Differential Equations155 (1999) 423-442. Zbl0946.35033MR1698561
3. [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. Zbl0835.35049MR1277103
4. [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. Zbl0901.35031MR1491858
5. [5] Crandall M.G., Rabinowitz P.H., Tartar L., On a Dirichlet problem with a singular nonlinearity, Comm. PDE2 (2) (1997) 193-222. Zbl0362.35031MR427826
6. [6] del Pino M.A., Radially symmetric layers in a semilinear elliptic system, Trans. Amer. Math. Soc.347 (1995) 4807-4837. Zbl0853.35009MR1303116
7. [7] Gui C., Multipeak solutions for a semilinear Neumann problem, Duke Math. J.84 ( 1996) 739-769. Zbl0866.35039MR1408543
8. [8] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, 1983. Zbl0562.35001MR737190
9. [9] Lazer A.C., McKenna P.J., On a singular nonlinear elliptic boundary value problem, Proc. Amer. Math. Soc.111 (1991) 721-730. Zbl0727.35057MR1037213
10. [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. Zbl0174.15403MR241822
11. [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. Zbl0453.76002
12. [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. Zbl0946.35007MR1639546
13. [13] Ni W.-M., Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc.45 (1998) 9-18. Zbl0917.35047MR1490535
14. [14] Protter M., Weinberger H., Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1984. Zbl0549.35002MR762825
15. [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). Zbl0885.35043MR1457293
16. [16] Sattinger D.H., Topics in Stability and Bifurcation Theory, Lecture Notes in Mathematics, Vol. 309, Springer-Verlag, 1973. Zbl0248.35003MR463624
17. [17] Serrin J., Zou H., Existence of positive entire solutions of elliptic Hamiltonian systems, Comm. Partial Differential Equations23 (1998) 577-599. Zbl0906.35033MR1620581
18. [18] Lair A., Wood A., Existence of entire solutions of semilinear elliptic systems, Preprint. 
19. [19] Stuart C.A., Existence theorems for a class of nonlinear integral equations, Math. Z.137 (1974) 49-66. Zbl0289.45013MR348416
20. [20] Taliaferro S.D., A nonlinear singular boundary value problem, Nonlinear Analysis TMA3 (1979) 897-904. Zbl0421.34021MR548961
21. [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.