|
|
Variational methods and linearization tools towards the spectral analysis of the p-Laplacian, especially for the Fredholm alternativeKeywords: Nonlinear eigenvalue problem , Fredholm alternative , degenerate or singular quasilinear Dirichlet problem , p-Laplacian , global minimizer , minimax principle Abstract: 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
|
