Noncoercive Resonant (p, 2)-Equations

We consider a nonlinear Dirichlet problem driven by the sumof p-Laplacian and a Laplacian (a (p, 2)-equation) which is resonant at +/-infinity with respect to the principal eigenvalue lambda(1)(p) of (-Delta(p), W-0(1, p) (Omega)) and resonant at zero with respect to any nonprincipal eigenvalue of (-Delta, H-0(1) (Omega)). At +/-infinity the resonance occurs from the right of lambda(1)(p) and so the energy functional of the problem is indefinite. Using critical groups, we show that the problem has at least one nontrivial smooth solution. The result complements the recent work of Papageorgiou and R. adulescu (Appl Math Optim 69: 393-430, 2014), where resonant (p, 2)-equations were examined with the resonance occurring from the left of lambda(1)(p) (coercive problem).