Unilateral global bifurcation for fourth-order eigenvalue problems with sign-changing weight

2012/07/31 by Guowei Dai, Dai, Guowei
Mathematics · #34B09 #34C10 #34C23 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:34B09 #msc:34C10 #msc:34C23

paper · pdf · doi:10.48550/arxiv.1207.7161

arXiv admin note: substantial text overlap with arXiv:1203.3262

arxiv created 2012/07/31 · arxiv updated 2012/08/01

Abstract

In this paper, we shall establish the unilateral global bifurcation result for a class of fourth-order eigenvalue problems with sign-changing weight. Under some natural hypotheses on perturbation function, we show that (μ_k^ν,0) is a bifurcation point of the above problems and there are two distinct unbounded continua, (C_k^ν)⁺ and (C_k^ν)^-, consisting of the bifurcation branch C_k^ν from (μ_k^ν, 0), where μ_k^ν is the k-th positive or negative eigenvalue of the linear problem corresponding to the above problems, ν∈+,-. As the applications of the above result, we study the existence of nodal solutions for a class of fourth-order eigenvalue problems with sign-changing weight. Moreover, we also establish the Sturm type comparison theorem for fourth-order problems with sign-changing weight.

Citations

• Unilateral global bifurcation and nodal solutions for the p-Laplacian with sign-changing weight

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