Affiliation:
1. Department of Basic Courses, Lanzhou Institute of Technology, Lanzhou 730050, China
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-+ratfx,0<t<1,x(0)=x(1)=x″(0)=x″(1)=0, wherer≠0is a parameter,a∈C([0,1],(0,∞)),x+=max{x,0},x-=-min{x,0},α,β∈C[0,1], andf∈C(R,R),sf(s)>0,fors≠0. We give the intervals for the parameterrwhich ensure the existence of nodal solutions for the above fourth-order half-linear problems iff0∈[0,∞)orf∞∈[0,∞],wheref0=lims→0f(s)/sandf∞=lims→+∞f(s)/s. We use the unilateral global bifurcation techniques and the approximation of connected components to prove our main results.
Funder
National Natural Science Foundation of China
Cited by
1 articles.
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