Basis properties of Fučík eigenfunctions for the Neumann Laplacian

Abstract

We investigate the basis properties of sequences of Fučík eigenfunctions of the one-dimensional Neumann Laplacian. We show that any such sequence is complete in L2(0,π) and a Riesz basis in the subspace of functions with zero mean. Moreover, we provide sufficient assumptions on Fučík eigenvalues which guarantee that the corresponding Fučík eigenfunctions form a Riesz basis in L2(0,π) and we explicitly describe the corresponding biorthogonal system.