Electron. J. Diff. Equ., Vol. 2014 (2014), No. 03, pp. 1-10.

Bifurcation from intervals for Sturm-Liouville problems and its applications

Guowei Dai, Ruyun Ma

Abstract:
We study the unilateral global bifurcation for the nonlinear Sturm-Liouville problem
$$\displaylines{ -(pu')'+qu=\lambda au+af(x,u,u',\lambda)+g(x,u,u',\lambda)\quad x\in(0,1),\cr b_0u(0)+c_0u'(0)=0,\quad b_1u(1)+c_1u'(1)=0, }$$
where $a\in C([0, 1], [0,+\infty))$ and $a(x)\not\equiv 0$ on any subinterval of $[0, 1]$, $f,g\in C([0,1]\times\mathbb{R}^3,\mathbb{R})$ and f is not necessarily differentiable at the origin or infinity with respect to u. Some applications are given to nonlinear second-order two-point boundary-value problems. This article is a continuation of [8].

Submitted September 8, 2013. Published January 3, 2014.
Math Subject Classifications: 34B24, 34C10, 34C23.
Key Words: Global bifurcation; nodal solutions; eigenvalues.

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Guowei Dai
Department of Mathematics
Northwest Normal University
Lanzhou 730070, China
email: daiguowei@nwnu.edu.cn
Ruyun Ma
Department of Mathematics
Northwest Normal University
Lanzhou 730070, China
email: mary@nwnu.edu.cn

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