Unilateral global bifurcation phenomena and nodal solutions for p-Laplacian

Abstract: 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 , we show that is a bifurcation point of the above problem and there are two distinct unbounded continua, and , consisting of the bifurcation branch from (), where 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) , we prove that there exist at least a positive solution and a negative one for the following problem [Copyright &y& Elsevier]