Unilateral global bifurcation phenomena and nodal solutions for p-Laplacian ✩
Unilateral global bifurcation phenomena and nodal solutions for p-Laplacian ✩
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DOI：
10.1016/j.jde.2011.09.026
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发表时间：
2012-02
影响因子：
2.4
通讯作者：
Guowei Dai;Ruyun Ma
中科院分区：
文献类型：
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作者：
Guowei Dai;Ruyun Ma
In this paper, we establish a Dancer-type unilateral global bifurcation result for one-dimensional p-Laplacian problem Under some natural hypotheses on the perturbation function g:(0,1)×R×R→R, we show that μk(p) is a bifurcation point of the above problem and there are two distinct unbounded continua, Ck+and Ck−, consisting of the bifurcation branch Ckfrom (μk(p),0), where μk(p) is the k-th eigenvalue of the linear problem corresponding to the above problem. As the applications of the above result, we study the existence of nodal solutions for the following problem Moreover, based on the bifurcation result of Girg and Takáč (2008) [13], we prove that there exist at least a positive solution and a negative one for the following problem
