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Zbl 1218.34027
Ma, Ruyun; Xu, Jia; Han, Xiaoling
Global bifurcation of positive solutions of a second-order periodic boundary value problem with indefinite weight.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 10, 3379-3385 (2011). ISSN 0362-546X

Summary: We are concerned with the global structure and stability of positive solutions to the periodic boundary value problem $$-u''(t)+q(t)u(t)=\lambda a(t)f(u(t)),\quad 0<t<2\pi,\quad u(0)=u(2\pi),\quad u'(0)=u'(2\pi),$$ where $q\in C(\Bbb R,[0,\infty))$ is of period $2\pi$ and $q(t)\equiv 0$, $t\in[0,2\pi]$; $a\in C(\Bbb R,\Bbb R)$ is of period $2\pi$ and changes sign. The proof of our main results are based on bifurcation techniques.
MSC 2000:
*34B18 Positive solutions of nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE
34C23 Bifurcation (periodic solutions)
34C25 Periodic solutions of ODE

Keywords: indefinite weight problem; bifurcation; positive periodic solutions

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