Abstract and Applied Analysis
Volume 4 (1999), Issue 3, Pages 195-208

Multiplicity of positive solutions to semilinear elliptic boundary value problems

Kenichiro Umezu

Faculty of Liberal Arts and Sciences, Maebashi Institute of Technology, Maebashi 371-0816, Japan

Received 12 September 1999

Copyright © 1999 Kenichiro Umezu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study semilinear elliptic boundary value problems of one parameter dependence where the number of positive solutions is discussed. Our main purpose is to characterize the critical value given by the infimum of such parameters for which positive solutions exist. Our approach is based on super- and sub-solutions, and relies on the topological degree theory on the positive cones of ordered Banach spaces. A concrete example is also presented.