In this note we consider bifurcation of positive solutions to the semilinear elliptic boundary-value problem with critical Sobolev exponent
where , is a bounded -domain , and is a bifurcation parameter. Brezis and Nirenberg  showed that a lower order (non-negative) perturbation can contribute to regain the compactness and whence yields existence of solutions. We study the equation with an indefinite perturbation and prove a bifurcation result of two solutions for this equation.
Submitted August 12, 2005. Published October 25, 2006.
Math Subject Classifications: 49K20, 35J65, 34B15.
Key Words: Critical Sobolev exponent; positive solutions; bifurcation.
Show me the PDF file (232K), TEX file, and other files for this article.
| Yuanji Cheng |
School of Technology and Society
SE-205 06 Malmo, Sweden
Return to the EJDE web page