Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-16T12:47:13.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence of solutions in a singular biharmonic nonlinear problem

Published online by Cambridge University Press:  20 January 2009

Gaston L. Hernandez  and
Y. Choi
Gaston L. Hernandez
Affiliation:
University of Connecticut, Storrs, CT 06269, USA
Y. Choi
Affiliation:
University of Connecticut, Storrs, CT 06269, USA
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.

In this work we prove the existence and uniqueness of positive solutions of the nonlinear singular boundary value problem

where 0<σ<1.

Extensions of the above results to the case of Δ2u−f(x, u) = 0 with appropriate singularity built into f are also given.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 3 , October 1993 , pp. 537 - 546
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

REFERENCES

1.Adams, Robert A., Sobolev Spaces (Academic Press, 1975).Google Scholar
2.Agmon, S., Douglis, A. and Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, Comm. Pure Appl. Math. 12 (1959), 623–727.CrossRefGoogle Scholar
3.Eloe, P. W. and Henderson, J., Nonlinear boundary value problems and apriori bounds on solutions. SIAM J. Math. Anal. (1984), 642–647.CrossRefGoogle Scholar
4.Friedman, Avner, Partial Differential Equations of Parabolic Type (Prentice-Hall, 1964).Google Scholar
5.Gilbaro, D. and Trudinger, N. S., Elliptic Partial Differential Equations of Second Order (Springer-Verlag, 1983).Google Scholar
6.Hernandez, Gaston E., Gatica, J. A., Fink, A. M. and Waltman, P., Approximations of solutions of singular second order boundary value problems, SIAM J. Math Anal. 22 (1989), 440–462.Google Scholar
7.Hernandez, Gaston E., Gatica, J. A. and Waltman, P., Radially symmetric solutions of a class of singular elliptic equations, Proc. Edinburgh Math. Soc. 33 (1989), 169–180.Google Scholar
8.Lazer, A. C. and Mck.Enna, P. J., On a singular nonlinear elliptic boundary-value problem. Proc. Amer. Math. Soc. 111 (1991), 721–730.Google Scholar
9.O'regan, Donal, Fourth (and higher) order singularity boundary value problems, Nonlinear Anal. 14 (1990), 1001–1038.CrossRefGoogle Scholar
10.Taliaferro, S., A nonlinear singular boundary value problem, Nonlinear Anal. 3 (1979), 897–904.CrossRefGoogle Scholar