Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T02:44:38.780Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic behaviour of small solutions of singularly perturbed problems

Published online by Cambridge University Press:  17 April 2009

Zongming Guo
Zongming Guo
Affiliation:
Department of Mathematics, Henan Normal University, Xinxiang, 453002, Peoples Republic of China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the singular limit of small solutions of some singularly perturbed problems where the nonlinearity changes sign.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 435 - 443
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Benci, V. and Cerami, G., ‘Multiple Positive solutions of some elliptic problems via the Morse theory and the domain topology’, Calc. Var. Partial Differential Equations 2 (1994), 29–48.CrossRefGoogle Scholar
[2]Berestycki, H. and Lions, P.L., ‘Nonlinear scalar field equations, I. Existence of a ground state’, Arch. Rational Mech. Anal. 82 (1983), 313–345.CrossRefGoogle Scholar
[3]Brezis, H. and Peletier, L.A., ‘Asymptotics for elliptic equations involving critical growth’, in Partial Differential Equations and the Calculus of Variations, (Colombini, F., Marino, A., Modica, L. and Spagnolo, S., Editors) (Birkhäuser, Basel, 1989), pp. 149–192.Google Scholar
[4]Dancer, E.N., ‘On positive solutions of some singularly perturbed problems where the nonlinearity changes sign”, Topol. Methods Nonlinear Anal. 5 (1995), 141–175.CrossRefGoogle Scholar
[5]Gidas, B., Ni, W.M. and Nirenberg, L., ‘Symmetry and related properties via the maximum principle’, Comm. Math. Phys. 68 (1979), 209–243.CrossRefGoogle Scholar
[6]Flucher, M. and Wei, J., ‘Asymptotic shape and location of small cores in elliptic free-boundary problems’, Math. Z. 228 (1998), 683–703.CrossRefGoogle Scholar
[7]Jang, J., ‘On spike solutions of singularly perturbed semilinear Dirichlet problems’ J. Diff. Equations 114 (1994), 370–395.CrossRefGoogle Scholar
[8]Merle, F. and Peletier, L.A., ‘Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth I. The radial case’, Arch. Rational Mech. Anal. 112 (1990), 1–19.CrossRefGoogle Scholar
[9]Ni, W.M. and Wei, J., ‘On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems’, Comm. Pure Appl. Math. 48 (1995), 731–768.CrossRefGoogle Scholar
[10]Ni, W.M., Takagi, I. and Wei, J., ‘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.CrossRefGoogle Scholar