Strong Resonance for Some Quasilinear Elliptic Equations1

We study the existence of the weak solutions of the nonlinear boundary value problem < < py2 yDpusl1u uqg u.yh x. in V, us0 on­V, where the nonlinearity g is of the Landesman]Lazer type. Our sufficient conditions generalize all previously published results about the strong resonance at the first eigenvalue.