Three solutions of a quasilinear elliptic problem near resonance (Q2702755)

Using critical point theory, the authors prove a multiplicity result near the first eigenvalue \(\lambda_1\) for quasilinear elliptic problems of the form NEWLINE\[NEWLINE -\Delta_pu-\lambda_1|u|^{p-2}u+\varepsilon |u|^{p-2}u=f(x,u)+h(x) NEWLINE\]NEWLINE with Dirichlet conditions. NEWLINENEWLINENEWLINEIt is proved that, for sufficiently small \(\varepsilon >0\), the problem above has at least three solutions when \(f\) and \(h\) satisfy a Landesman-Lazer condition.