In Theorem 15.4, the bifurcation theorem of nonlinear Sturm-Liouville eigenvalue problems Lu = F (sBC), which concluded the previous chapter, a key hypothesis was the invertibility of Lu = - (pu′)′ + qu with respect to the given boundary conditions. Certainly a necessary condition for an operator to be invertible is that it be one-to-one.


Bifurcation Point Nontrivial Solution Zero Function Previous Chapter Bifurcation Theorem 
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© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Robert F. Brown
    • 1
  1. 1.Department of MathematicsUniversity of California, Los AngelesLos AngelesUSA

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