Article ID Journal Published Year Pages File Type
6415152 Journal of Functional Analysis 2013 17 Pages PDF
Abstract

In this paper, we shall establish the unilateral global bifurcation which bifurcates from the trivial solutions axis or from infinity of a class of nonlinear Sturm-Liouville problems with nondifferentiable nonlinearity, respectively. As applications of the above results, we shall determine the interval of r, in which there exist nodal solutions for the following problem{u″(t)+ra(t)f(u)=0,t∈(0,1),u(0)=u(1)=0, where a(t) is a positive continuous function on [0,1], f∈C(R,R) but is not necessarily differentiable at the origin and infinity. Moreover, as a special case of the above problem, we shall prove more details about the existence of nodal solutions for a class of half-linear eigenvalue problems.

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Physical Sciences and Engineering Mathematics Algebra and Number Theory
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