On The Second Eigenvalue For Nonhomogeneous Quasi-linear Operators
Stephen B. Robinson · SIAM Journal on Mathematical Analysis · 2004
In this paper we study a nonlinear eigenvalue problem and associated perturbations of the problem. More specifically, we generalize a variational characterization of the second eigenvalue for homogenous quasi-linear elliptic operators, such as the p-Laplacian, to a class of nonhomogeneous quasi-linear elliptic operators. Neumann boundary data is assumed throughout the paper. To demonstrate the utility of this characterization we use it to prove a generalized Fredholm alternative for nonresonant perturbations of the given eigenvalue problem.