Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T17:31:59.418Z Has data issue: false hasContentIssue false
  • English
  • Français

UNIQUENESS FOR SINGULAR SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS

Published online by Cambridge University Press:  25 February 2013

D. D. HAI  and
R. C. SMITH
D. D. HAI
Affiliation:
Department of Mathematics, Mississippi State UniversityMississippi State, MS 39762, USA e-mail: [email protected], [email protected]
R. C. SMITH
Affiliation:
Department of Mathematics, Mississippi State UniversityMississippi State, MS 39762, USA e-mail: [email protected], [email protected]
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 prove uniqueness of positive solutions for the boundary value problems

\[ \{\begin{array}{ll} -\Delta u=\lambda f(u)\ \ &\text{in}\Omega, \ \ \ \ \ u=0 &\text{on \partial \Omega, \]
where Ω is a bounded domain in ℝn with smooth boundary ∂Ω, λ is a positive parameter and f:(0,∞) → (0,∞) is sublinear at ∞ and is allowed to be singular at 0.

Keywords

35J7535J92
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 2 , May 2013 , pp. 399 - 409
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013

References

REFERENCES

1.Crandall, M. G., Rabinowitz, P. H. and Tarta, L., On a Dirichlet problem with a singular nonlinearitiy, Comm. Partial Differ. Equ. 2 (1977), 193–222.Google Scholar
2.Dancer, E. N., On the number of positive solutions of semilinear elliptic systems, Proc. Lond. Math. Soc. 53 (1986), 429–452.Google Scholar
3.Hai, D. D., On a class of singular p-Laplacian boundary value problems, J. Math. Anal. Appl. 383 (2011), 619–626.Google Scholar
4.Hai, D. D. and Smith, R. C., On uniqueness for a class of nonlinear boundary value problems, Proc. Roy. Soc. Edinburgh A 136A (2006), 779–784.CrossRefGoogle Scholar
5.Lin, S. S., On the number of positive solutions for nonlinear elliptic equations when a parameter is large, Nonlinear Anal. 16 (1991), 283–297.Google Scholar
6.Sakaguchi, S., Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 14 (1987), 403–421.Google Scholar
7.Schuchman, V., About uniqueness for nonlinear boundary value problems, Math. Ann. 267 (1984), 537–542.Google Scholar
8.Walter, W., A theorem on elliptic differential inequalities with an application to gradient bounds, Math. Z. 200 (1989), 293–299.CrossRefGoogle Scholar
9.Wiegner, M., A uniqueness theorem for some nonlinear boundary value problems with a large parameter, Math. Ann. 270 (1985), 401–402.CrossRefGoogle Scholar