Speaker: Francesco TUDISCO (Gran Sasso Science Institute, L'Aquilla, Italy)

Time： May 25, 16:00-17:00

Place： ZOOM ID: 942 6323 4612 Passcode: 713982

Title： Nodal domain count of the generalized p-Laplacian on graphs

Abstract： We consider a generalized p-Laplacian operator on discrete graphs which generalizes the linear Schrödinger operator (obtained for p=2). We consider a set of variational eigenvalues of this operator and present new results that characterize several spectral properties of this operator with particular attention to the nodal domain count of its eigenfunctions. Just like the one-dimensional continuous p-Laplacian, we prove that the variational spectrum of the discrete generalized p-Laplacian on forests is the entire spectrum. Moreover, we show how to transfer the Weyl’s inequalities for the Laplacian operator to the nonlinear case and thus we prove new upper and lower bounds on the number of nodal domains of every eigenfunction of the generalized p-Laplacian on graphs, including those corresponding to variational eigenvalues. When applied to the linear case p=2, the new results imply well-known properties of the linear Schrödinger operator as well as novel ones.