We present a new approach to studying a class of quasilinear problems including the so-called Modified Nonlinear Schrödinger Equations (MNLS). We show that solutions of quasilinear equations can be obtained as limits of -Laplacian perturbations.

We consider the problem - Δ p ⁢ u + a ⁢ ( x ) ⁢ | u | p - 2 ⁢ u = | u | q - 2 ⁢ u {-\Delta_{p}u+a(x)\lvert u\rvert^{p-2}u=\lvert u\rvert^{q-2}u} in ℝ N {\mathbb{R}^{N}} , where 1 < p < N {1<p<N} , p < q < p * = N ⁢ p N - p {p<q<p^{*}=\frac{Np}{N-p}} , Δ p {\Delta_{p}} is the p -Laplacian operator, and the potential function a is positive, bounded and verifies suitable decay assumptions. The existence of infinitely many solutions of the equation is proved via the truncation method.

We consider the existence of infinitely many solutions of a class of quasilinear problems, for which the corresponding functionals are non-symmetric