The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
In this paper, we are concerned with the global structure and stability of positive solutions of periodic boundary value problem −u″(t)+q(t)u(t)=λa(t)f(u(t)),0<t<2π,u(0)=u(2π),u′(0)=u′(2π), where q∈C(R,[0,∞)) is of periodic 2π and q(t)≢0,t∈[0,2π]; a∈C(R,R) is of periodic 2π and changes sign. The proof of our main results are based on bifurcation techniques.