On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem: Intermediate solutions
Wei-Ming Ni, Izumi Takagi, and Juncheng Wei
Source: Duke Math. J. Volume 94, Number 3
(1998), 597-618.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077230459
Mathematical Reviews number (MathSciNet): MR1639546
Zentralblatt MATH identifier: 0946.35007
Digital Object Identifier: doi:10.1215/S0012-7094-98-09424-8
References
[1] A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349–381.
Mathematical Reviews (MathSciNet): MR51:6412
Zentralblatt MATH: 0273.49063
Digital Object Identifier: doi:10.1016/0022-1236(73)90051-7
[2] P. Clément and G. Sweers, Existence and multiplicity results for a semilinear elliptic eigenvalue problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987), no. 1, 97–121.
Mathematical Reviews (MathSciNet): MR89j:35053
Zentralblatt MATH: 0662.35045
[3] R. A. Fisher, The advance of advantageous genes, Ann. of Eugenics 7 (1937), 355–369.
Zentralblatt MATH: 63.1111.04
[4] R. Gardner and L. A. Peletier, The set of positive solutions of semilinear equations in large balls, Proc. Roy. Soc. Edinburgh Sect. A 104 (1986), no. 1-2, 53–72.
Mathematical Reviews (MathSciNet): MR88e:35063
Zentralblatt MATH: 0625.35030
[5] B. Gidas, W.-M. Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), no. 3, 209–243.
Mathematical Reviews (MathSciNet): MR80h:35043
Zentralblatt MATH: 0425.35020
Digital Object Identifier: doi:10.1007/BF01221125
Project Euclid: euclid.cmp/1103905359
[6] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Grundlehren Math. Wiss., vol. 224, Springer-Verlag, Berlin, 1983.
Mathematical Reviews (MathSciNet): MR86c:35035
Zentralblatt MATH: 0562.35001
[7] J. Jang, On spike solutions of singularly perturbed semilinear Dirichlet problem, J. Differential Equations 114 (1994), no. 2, 370–395.
Mathematical Reviews (MathSciNet): MR95i:35099
Zentralblatt MATH: 0812.35008
Digital Object Identifier: doi:10.1006/jdeq.1994.1154
[8] J. Jang, 1994, private communication.
[9] W. S. Massey, A basic course in algebraic topology, Graduate Texts in Mathematics, vol. 127, Springer-Verlag, New York, 1991.
Mathematical Reviews (MathSciNet): MR92c:55001
Zentralblatt MATH: 0725.55001
[10] W.-M. Ni and I. Takagi, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 44 (1991), no. 7, 819–851.
Mathematical Reviews (MathSciNet): MR92i:35052
Zentralblatt MATH: 0754.35042
Digital Object Identifier: doi:10.1002/cpa.3160440705
[11] W.-M. Ni and I. Takagi, Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993), no. 2, 247–281.
Mathematical Reviews (MathSciNet): MR94h:35072
Zentralblatt MATH: 0796.35056
Digital Object Identifier: doi:10.1215/S0012-7094-93-07004-4
Project Euclid: euclid.dmj/1077290699
[12] W.-M. Ni and J. Wei, On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math. 48 (1995), no. 7, 731–768.
Mathematical Reviews (MathSciNet): MR96g:35077
Zentralblatt MATH: 0838.35009
Digital Object Identifier: doi:10.1002/cpa.3160480704
[13] L. A. Peletier and J. Serrin, Uniqueness of positive solutions of semilinear equations in $\bf R\spn$, Arch. Rational Mech. Anal. 81 (1983), no. 2, 181–197.
Mathematical Reviews (MathSciNet): MR84b:35046
Zentralblatt MATH: 0516.35031
Digital Object Identifier: doi:10.1007/BF00250651
[14] J. Wei, On the effect of domain geometry in singular perturbation problems, preprint, 1996.
Mathematical Reviews (MathSciNet): MR1811947
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