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Global bifurcation of positive solutions of a second-order periodic boundary value problem with indefinite weight. (English) Zbl 1218.34027

Summary: We are concerned with the global structure and stability of positive solutions to the periodic boundary value problem

$-{u}^{\text{'}\text{'}}\left(t\right)+q\left(t\right)u\left(t\right)=\lambda a\left(t\right)f\left(u\left(t\right)\right),\phantom{\rule{1.em}{0ex}}0

where $q\in C\left(ℝ,\left[0,\infty \right)\right)$ is of period $2\pi$ and $q\left(t\right)\equiv 0$, $t\in \left[0,2\pi \right]$; $a\in C\left(ℝ,ℝ\right)$ is of period $2\pi$ and changes sign. The proof of our main results are based on bifurcation techniques.

##### MSC:
 34B18 Positive solutions of nonlinear boundary value problems for ODE 34B15 Nonlinear boundary value problems for ODE 34C23 Bifurcation (ODE) 34C25 Periodic solutions of ODE