Basis properties of Fučik eigenfunctions (Q2166131)

The paper deals with the Fučik eigenvalue problem \[ \begin{gathered} -u''(x)=\alpha u^+(x)-\beta u^-(x), \text{ in } (0,\pi), \\ u(0)=u(\pi)=0, \end{gathered} \tag{1} \] where \(\alpha\) and \(\beta\) are spectral parameters. The authors establish explicit formulas for the norms of the normalized Fučik eigenfunctions of problem (1), and their distances to the corresponding sine functions. Then they obtain sequences of Fučik eigenvalues \((\alpha(n),\beta(n))\) for which the corresponding eigenfunctions form a Riesz basis in \(L^2(0,\pi)\).