Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications
| Autor: | Wenguo Shen, Tao He |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Discrete Dynamics in Nature and Society, Vol 2016 (2016) |
| Druh dokumentu: | article |
| ISSN: | 1026-0226 1607-887X |
| DOI: | 10.1155/2016/5956713 |
| Popis: | 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-+ratfx, 00, 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=lims→0f(s)/s and f∞=lims→+∞f(s)/s. We use the unilateral global bifurcation techniques and the approximation of connected components to prove our main results. |
| Databáze: | Directory of Open Access Journals |
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