Hostname: page-component-7c8c6479df-p566r Total loading time: 0 Render date: 2024-03-28T07:56:25.452Z Has data issue: false hasContentIssue false

Liouville-type results for fourth order elliptic equations

Published online by Cambridge University Press:  14 November 2011

Vinod B. Goyal
Affiliation:
Department of Mathematics, Tuskegee University, Tuskegee, AL 36088, U.S.A.

Synopsis

Liouville type theorems are obtained for the solutions to elliptic equations of the form Δ2u −q(x)Δu + p(x)f(u)=0 by means of two subharmonic functionals and Green type inequalities.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1986

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

1Goyal, V. B. and Schaeffer, P. W.. Liouville theorems for a class of fourth order ellipticequations. Proc. Roy. Soc. Edinburgh Sect. A 86 (1980), 129137.CrossRefGoogle Scholar
2Goyal, V. B. and Schaeffer, P. W.. Liouville theorems for elliptic systems and nonlinear equations of fourth order. Proc. Roy. Soc. Edinburgh Sect. A 91 (1982), 235242.CrossRefGoogle Scholar
3Protter, M. H. and Weinberger, H. F.. Maximum principles in differential equations (Englewood Cliffs, N.J.: Prentice Hall, 1967).Google Scholar