Discrete analogue of Fučík spectrum of the Laplacian (Q1300732)

The Fučík spectrum of the Laplacian with a Dirichlet boundary condition \((-\Delta u=\alpha u^+-\beta u^-)\) and the discrete analog of the Fučík spectrum for the matrix \(A\) \((M\)-matrices) are considered. This analog has properties similar to those of the continuum. The Fučík spectrum of an \(M\)-matrix contains a continuous and decreasing curve which is symmetric with respect to the diagonal. The role of the function \(\psi(x)= \langle Ax,x \rangle-\lambda_1\|x\|^2\) on the discrete analog is studied.