Electronic Journal of Differential Equations (Aug 2015)

Multiple solutions for Kirchhoff type problem near resonance

  • Shu-Zhi Song,
  • Chun-Lei Tang,
  • Shang-Jie Chen

Journal volume & issue
Vol. 2015, no. 215,
pp. 1 – 7

Abstract

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Based on Ekeland's variational principle and the mountain pass theorem, we show the existence of three solutions to the Kirchhoff type problem $$\displaylines{ -\Big(a+b\int_{\Omega}|\nabla u|^2dx \Big) \Delta u =b \mu u^3+f(x,u)+h(x), \quad\text{in } \Omega, \cr u=0, \quad \text{on } \partial \Omega. }$$ Where the parameter $\mu$ is sufficiently close, from the left, to the first nonlinear eigenvalue.

Keywords