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We look for weak solutions $uin W_0^{1,p}(Omega)$ of the degenerate quasilinear Dirichlet boundary value problem $$ eqno{(P)} - Delta_p u = lambda |u|^{p-2} u + f(x) quad hbox{in } Omega ,;quad u = 0 quad hbox{on } partialOmega ,. $$ It is assumed that $1<p<infty$, $p eq 2$, $Delta_p uequiv hbox{div} ( | abla u|^{p-2} abla u )$ is the p-Laplacian, $Omega$ is a bounded domain in ${mathbb{R}}^N$, $fin L^infty(Omega)$ is a given function, and $lambda$ stands for the (real) spectral parameter. Such weak solutions are precisely the critical points of the corresponding energy functional on $W_0^{1,p}(Omega)$, $$ eqno{(J)} mathcal{J}_{lambda}(u) := frac{1}{p} int_Omega | abla u|^p ,dx - frac{lambda}{p} int_Omega |u|^p ,dx - int_Omega f(x), u,dx ,,quad uin W_0^{1,p}(Omega) ,. $$ I.e., problem (P) is equivalent with $mathcal{J}_{lambda}'(u) = 0$ in $W^{-1,p'}(Omega)$. Here, $mathcal{J}_{lambda}'(u)$ stands for the (first) Frechet derivative of the functional $mathcal{J}_{lambda}$ on $W_0^{1,p}(Omega)$ and $W^{-1,p'}(Omega)$ denotes the (strong) dual space of the Sobolev space $W_0^{1,p}(Omega)$, $p'= p/(p-1)$.