Soliton solutions for zero-mass (<i>N</i>, <i>q</i>)-Laplacian equations with critical exponential growth in RN

We study the following class of quasilinear zero-mass (N, q)-Laplacian equations proposed in plasma physics and nonlinear optics −ΔNu−uΔN(u2)−Δqu−uΔq(u2)=Q(x)f(u),x∈RN, where Δru = div(|∇u|r−2∇u) denotes the usual r-Laplacian operator with r ∈ {q, N} and 1&amp;lt;q≤N2, Q∈C0(RN;R) is a positive function satisfying some technical assumptions and f fulfills the critical exponential growth in the Trudinger-Moser sense at infinity. With the help of change of variables, we investigate the existence of nontrivial solutions by analysing its associated “limiting equation.”