Persistence and Bifurcation of Degenerate Solutions

  title={Persistence and Bifurcation of Degenerate Solutions},
  author={Junping Shi},
  journal={Journal of Functional Analysis},
  • Junping Shi
  • Published 20 December 1999
  • Mathematics
  • Journal of Functional Analysis
Abstract We consider a nonlinear equation F ( e ,  λ ,  u )=0, where F is a differentiable mapping from R × R × X to Y and X ,  Y are Banach spaces. When e varies from a fixed e = e 0 , bifurcation occurs to the solution curve ( λ ( s ),  u ( s )). We study the degenerate solutions of the equation, and we obtain several bifurcation theorems on the degenerate solutions, which can be applied in many nonlinear problems to obtain precise global bifurcation diagrams. 

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