Multiplicity of solutions for quasilinear elliptic equations

The semilinear elliptic equation −∆u = g(x, u) has been the object of several studies in the last twenty years. For instance, let us mention the well-known result proved by Ambrosetti and Rabinowitz (cf. [1]): if g is superlinear and odd with respect to the second variable, then the above equation has a sequence of solutions uh ∈ H 0 (Ω) with ‖uh‖H1 0 →∞. In order to get such a result, a variational technique has been employed. In fact, the above equation is the Euler equation associated with the functional f(u) = 1 2 ∫