Extent of the Left-Branching Solution to Certain Bifurcation Problems

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Abstract

A special class of nonlinear eigenvalue problems which exhibit branching to the left of. (below) the smallest eigenvalue is considered. This particular class serves to illustrate a procedure for bounding the leftward extent of a nonnegative solution branch. The procedure relies upon a well-known result about upper and lower solutions associated with a monotone operator. In the situation of left-branching bifurcation, the more difficult determination of a suitable lower solution is achieved by using an explicit solution to a simpler nonlinear problem. A physical example relative to the buckling of a nonlinearly elastic rod is worked out in detail.
Original languageEnglish
Pages (from-to)392-401
JournalSIAM Journal on Mathematical Analysis
Volume8
DOIs
StatePublished - 1977

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