On nonlinear nonhomogeneous resonant Dirichlet equations

We consider a ( p, 2)-equation with a Carathéodory reaction f (z, x) which is resonant at ±∞ and has constant sign, z-dependent zeros.Using variational methods, together with truncation and comparison techniques and Morse theory, we establish the existence of five nontrivial smooth solutions (four of constant sign and the fifth nodal).If the reaction f (z, x) is C 1 in x ∈ ‫,ޒ‬ then we produce a second nodal solution for a total of six nontrivial smooth solutions.