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We review multiplicity results for semilinear and quasilinear boundary value problems due to the presence of zeros of the nonlinearity. Most of their proofs rely on the global bifurcation theorem, the bifurcation from infinity, and the bifurcation from simple eigenvalues. The zeros of the nonlinearity play a crucial role in separating branches emanating from infinity from those emanating from zero.

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The Zeros of Nonlinearities and Multiplicity of Solutions for Nonlinear Elliptic Problems

  • 会议论文

  • 发表日期：

    2026年

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  • Alfonso Castro,
  • Jorge Cossio,
  • Sigifredo Herrón,
  • Carlos Vélez

摘要

We review multiplicity results for semilinear and quasilinear boundary value problems due to the presence of zeros of the nonlinearity. Most of their proofs rely on the global bifurcation theorem, the bifurcation from infinity, and the bifurcation from simple eigenvalues. The zeros of the nonlinearity play a crucial role in separating branches emanating from infinity from those emanating from zero.