Bifurcation of positive solutions from zero or infinity in elliptic problems which are not linearizable

Bryan Patrick Rynne, Martin Alexander Youngson

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The existence of global continua of solutions bifurcating from u = 0 on `bifurcation intervals' surrounding the eigenvalues of the linear problem obtained by putting the nonlinear term equal to zero is proven. These continua have similar properties obtained in Rabinowitz' global bifurcation theorem. The elliptic partial differential problem was also considered in [3], where it was shown that, when M1 = 0, continua of positive or negative solutions bifurcate from an interval containing the principal eigenvalue. The Sturm-Liouville analogue of (1.1) was studied and extended the previous results to deal with bifurcation from either u = 0 or u = 8, for the general case M1<0.

Original languageEnglish
Pages (from-to)21-31
Number of pages11
JournalNonlinear Analysis: Theory, Methods and Applications
Volume44
Issue number1
DOIs
Publication statusPublished - Mar 2001

Fingerprint Dive into the research topics of 'Bifurcation of positive solutions from zero or infinity in elliptic problems which are not linearizable'. Together they form a unique fingerprint.

  • Cite this