NONLINEAR EIGENCURVES AND APPLICATIONS TO THE STUDY OF THE STRICT MONOTONY OF THE SECOND EIGENVALUE FOR THE p -LAPLACIAN WITH WEIGHT

摘要

In this paper we are interested to the study of the so called eigencurves associated to the following nonlinear problem G′(u) = αF′(u) + βH′(u), under some conditions on F, G and H. Thus we show that the set C_n = {(α, β) ∈ IR~2 / λ_n(αF + βH, G) = 1} is the graph of some curve. The study of the local strict monotony of C_n is also considered. We will give an application to the study of the strict monotony of the second eigenvalue for the p-Laplacian with weight.