Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-12T22:23:48.245Z Has data issue: false hasContentIssue false
  • English
  • Français

On a singular nonlinear semilinear elliptic problem

Published online by Cambridge University Press:  14 November 2011

Junping Shi  and
Miaoxin Yao
Junping Shi
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602-6539, U.S.A.
Miaoxin Yao
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602-6539, U.S.A., and Department of Mathematics, Tianjin University, Tainjin 300072, P.R. China
Get access Rights & Permissions [Opens in a new window]

Extract

We consider the singular boundary value problem

We study the existence, uniqueness, regularity and the dependency on parameters of the positive solutions under various assumptions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 6 , 1998 , pp. 1389 - 1401
Copyright
Copyright © Royal Society of Edinburgh 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Ambrosetti, A., Brezis, H. and Cerami, G.. Combined effects of concave and convex nonlinearities in some elliptic problems. J. Funct. Anal. 122 (1994), 519–43.Google Scholar
2Brezis, H. and Kamin, S.. Sublinear elliptic equations in ℝn. Manuscripta Math. 74 (1992), 87–106.CrossRefGoogle Scholar
3Callegari, A. and Nashman, A.. A nonlinear singular boundary value problem in the theory of pseudoplastic fluids. SIAM J. Appl. Math. 38 (1980), 275–81.Google Scholar
4Coclite, M. M. and Palmieri, G.. On a singular nonlinear Dirichlet problem. Comm. Partial Differential Equations 14(1989), 1315–27.Google Scholar
5Cohen, D. S. and Keller, H. B.. Some positive problems suggested by nonlinear heat generators. J. Math. Meek 16 (1967), 1361–76.Google Scholar
6Crandall, M. G., Rabinowitz, P. H. and Tartar, L.. On a Dirichlet problem with a singular nonlinearity. Comm. Partial Differential Equations 2 (1977), 193–222.Google Scholar
7Pino, M. Del. A global estimate for the gradient in a singular elliptic boundary value problem. Proc. Roy. Soc. Edinburgh Sect. A 122 (1992), 341–52.Google Scholar
8Diaz, J. I., Morel, J. M. and Oswald, L.. An elliptic equation with singular nonlinearity. Comm. Partial Differential Equations 12 (1987), 1333–44.CrossRefGoogle Scholar
9Fulks, W. and Maybee, J. S.. A singular nonlinear equation. Osaka Math. J. 12 (1960), 1–19.Google Scholar
10Gomes, S. M.. On a singular nonlinear elliptic problem. SI AM J. Math. Anal. 17 (1986), 1359–69.CrossRefGoogle Scholar
11Gilberg, D. and Trudinger, N. S.. Elliptic Partial Differential Equations of Second Order, 2nd edn (Berlin: Springer, 1983).Google Scholar
12Gui, C. and Lin, F.. Regularity of an elliptic problem with a singular nonlinearity. Proc. Roy. Soc. Edinburgh Sect. A 123 (1993), 1021–9.Google Scholar
13Lazer, A. C. and McKenna, P. J.. On a singular nonlinear elliptic boundary value problem. Proc. Amer. Math. Soc. 3 (1991), 720–30.Google Scholar
14Ouyang, T., Shi, J. and Yao, M.. Exact multiplicity of positive solutions for a singular differential equation (Preprint, 1996).Google Scholar
15Stuart, C. A.. Existence and approximation of solutions of nonlinear elliptic equations. Math. Z. 147 (1976), 53–62.CrossRefGoogle Scholar
16Shi, J. and Yao, M.. Positive solutions of elliptic equations with singular nonlinearity (submitted, 1996).Google Scholar
17Zhang, Z.. On a Dirichlet problem with a singular nonlinearity. J. Math. Anal. 194 (1995), 103–13.Google Scholar