Vol. 44, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
A nonlinear elliptic boundary value problem

Stephen Andrew Williams

Vol. 44 (1973), No. 2, 767–774
Abstract

This paper proves that there is a (weak) solution u (not necessarily unique) to the generalized Dirichlet problem (with null boundary data) for the equation Au + pu = h. Here A is a strongly and uniformly elliptic operator of order 2m on a bounded open set Ω Rn. Also A is “normal”: roughly, AA = AA. The functions p and h are bounded and continuous, but are allowed to depend on x(x Ω),u, and the generalized derivatives of u up to order m. The values of p are restricted to lie in a closed disk of the complex plane which contains the negative of no weak eigenvalue of A.

Mathematical Subject Classification 2000
Primary: 35J60
Milestones
Received: 13 September 1971
Published: 1 February 1973
Authors
Stephen Andrew Williams