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

Wenguo Shen and Tao He

Discrete Dynamics in Nature and Society, 2016, vol. 2016, issue 1

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: x″″ = αx+ + βx− + ra(t)f(x), 0 0, for s ≠ 0. We give the intervals for the parameter r which ensure the existence of nodal solutions for the above fourth‐order half‐linear problems if f0 ∈ [0, ∞) or f∞ ∈ [0, ∞], where f0 = lim|s|→0f(s)/s and f∞ = lim|s|→+∞f(s)/s. We use the unilateral global bifurcation techniques and the approximation of connected components to prove our main results.

Date: 2016
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https://doi.org/10.1155/2016/5956713

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnddns:v:2016:y:2016:i:1:n:5956713

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