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Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications

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  • Wenguo Shen
  • Tao He

Abstract

We establish a unilateral global bifurcation result from interval for a class of fourth-order problems with nondifferentiable nonlinearity. By applying the above result, we firstly establish the spectrum for a class of half-linear fourth-order eigenvalue problems. Moreover, we also investigate the existence of nodal solutions for the following half-linear fourth-order problems: , , , where is a parameter, , , , , and , for . We give the intervals for the parameter which ensure the existence of nodal solutions for the above fourth-order half-linear problems if or where and . We use the unilateral global bifurcation techniques and the approximation of connected components to prove our main results.

Suggested Citation

  • Wenguo Shen & Tao He, 2016. "Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-15, March.
    • Handle: RePEc:hin:jnddns:5956713
    DOI: 10.1155/2016/5956713
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