Linked eigenvalue problems for the p -Laplacian

Source abstract

Linked equations of the form are studied on a bounded smooth domain in R N for λ ∈ R 2 . Existence and uniqueness of solutions are discussed for f i homogeneous of order p – 1 in u i , generalising the ‘Klein Oscillation Theorem’ when p = 2, N = 1. Bifurcation from the principal eigenvalue is also considered for nonhomogeneous perturbations f i of order greater than p – 1.