References
- Nakashima , K . 2000 . Stable transition layers in a balanced bistable equation . Differ. Integral Equ. , 13 : 1025 – 1038 .
- Matsuzawa , H . 2004 . Stable transition layers in a balanced bistable equation with degeneracy . Nonlinear Anal. , 58 : 45 – 67 .
- Nakashima , K . 2003 . Multi-layered stationary solutions for a spatially inhomogeneous Allen-Cahn equation . J. Differ. Equ. , 191 : 234 – 276 .
- Nakashima , K and Tanaka , K . 2003 . Clustering layers and boundary layers in spatially inhomogeneous phase transition problems . Ann. Inst. H. Poincaré. Non Linéaire , 20 : 107 – 143 .
- Dancer , N and Yan , S . 2003 . Multi-layer solutions for an elliptic problem . J. Differ. Equ. , 194 : 382 – 405 .
- Matano , H . 1979 . Asymptotic behavior and stability of solutions of semilinear differential equations . Publ. Res. Inst. Math. Sci. , 15 ( 2 ) : 401 – 454 .
- do Nascimento , AS . 1997 . Local minimizers induced by spatial inhomogeneity with inner transition layer . J. Differ. Equ. , 133 : 203 – 223 .
- Yeh , L-C and Norbury , J . 2007 . Variational problems with singular perturbation . Nonlinear Anal. , 66 : 51 – 61 .
- do Nascimento , AS . 1999 . On the role of diffusivity in some stable equilibria of a diffusive equation . J. Differ. Equ. , 155 : 231 – 244 .
- Furter , JE and López-Gómez , J . 1997 . Diffusion-mediated permanence problem for a heterogeneous Lotka-Voltera competition model . Proc. R. Soc. Edinb. A , 127 : 281 – 336 .
- Daners , D and López-Gómez , J . 1994 . The singular perturbation problem for the periodic-parabolic logistic equation with indefinite weight functions . J. Dyn. Differ. Equ. , 6 : 659 – 670 .
- Amann , H . 1971/72 . On the existence of positive solutions of nonlinear elliptic boundary value problems . Indiana Univ. Math. J. , 21 : 125 – 146 .
- Berestycki , H and Lions , PL . 1980 . Some Applications of the Methods of Super and Subsolutions, Bifurcations and Nonlinear Eigenvalue Problems (Proc. Session, Univ. Paris XIII, Villetaneuse, 1978), Lecture Notes in Mathematics , Vol. 782 , Berlin : Springer .
- Dancer , N and Yan , S . 2004 . Construction of various types of solutions for an elliptic problem . Calc. Var. Partial Differ. Equ. , 20 : 93 – 118 .
- Yan , S . 2005 . personal communication
- Du , Y . 2006 . Order Structure and Topological Methods in Nonlinear Partial Differential Equations , Vol. 1 , Singapore : World Scientific .
- Bandle , C and Marcus , M . 1992 . Large solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behavior . J. Anal. Math. , 58 : 9 – 24 .
- Keller , JB . 1957 . On solutions of Δu = f(u) . Commun. Pure Appl. Math. , 10 : 503 – 510 .
- Osserman , R . 1957 . On the inequality Δu ≥ f(u) . Pac. J. Math. , 7 : 1641 – 1647 .
- Zhang , Z . 2006 . Existence of large solutions for a semilinear elliptic problem via explosive sub-supersolutions . Electron. J. Differ. Equ. , 2006 : 1 – 8 .
- Du , Y and Huang , Q . 1999 . Blow-up solutions for a class of semilinear elliptic and parabolic equations . SIAM J. Math. Anal. , 31 : 1 – 18 .
- Gómez-Renasco , R and López-Gómez , J . 2002 . On the existence and numerical computations of classicla and non-classical solutions for a family of elliptic boundary value problems . Nonlinear Anal. , 48 : 567 – 605 .
- López-Gómez , J . 2005, Chapter 4 . “ Malthus versus Verhulst in population dynamics: A dream of Volterra ” . In Handbook of Differential Equations ‘Stationary Partial Differential Equations’ , Edited by: Chipt , M and Quittner , P . 211 – 209 . North Holland, Amsterdam : Elsevier Science B.V. .
- García-Melián , J , Letelier-Albornoz , R and Sabina de Lis , J . 2001 . Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up . Proc. Amer. Math. Soc. , 129 ( 12 ) : 3593 – 3602 .
- Brezis , H and Nirenberg , L . 1993 . H 1 versus C 1 local minimizers . C. R. Acad. Sci. Paris Ser. I , 317 : 465 – 472 .
- do Nascimento , AS . 2003 . Stable transition layers in a semilinear diffusion equation with spatial inhomogeneities in N- dimensional domains . J. Differ. Equ. , 190 : 16 – 38 .
- García-Melián , J and Sabina de Lis , JC . 2000 . Stationary profiles of degenerate profiles of degenerate problems when parameter is large . Differ. Integral. Equ. , 13 : 1201 – 1232 .
- Fraile , JM , López-Gómez , J and Sabina de Lis , JC . 1995 . On the global structure of the set of positive solutions of some semilinear elliptic boundary value problems . J. Differ. Equ. , 123 : 180 – 212 .
- Shibata , T . 2004 . The steepest point of the boundary layers of singularly perturbed semilinear elliptic problems . Trans. Amer. Math. Soc. , 356 : 2123 – 2135 .
- Norbury , J and Yeh , L-C . 2001 . The location and stability of interface solutions of an inhomogeneous parabolic problem . SIAM J. Appl. Math. , 61 : 849 – 862 .
- Gilbarg , D and Trudinger , N . 1983 . Elliptic Partial Differential Equations of Second Order , Berlin : Springer .
- Gidas , B , Ni , WM and Nirenberg , L . 1979 . Symmetry and related properties via the maximum principle . Commun. Math. Phys. , 68 : 209 – 243 .