Concentration of solutions for an (N, q)-Laplacian equation with Trudinger-Moser nonlinearity.

In this article, we consider the concentration of positive solutions for the following equation with Trudinger-Moser nonlinearity: ∫-∆Nu - ∆qu + V(εx)(|u|N-2u + |u|q-2u) = f(u), x ∈ RN, u ∈ W1,N(RN) ∩ W1,q(RN), x ∈ RN, where V is a positive continuous function and has a local minimum, ε > 0 is a small parameter, 2 ≤ N < q < +∞, f is C¹ with subcritical growth. When V and f satisfy some appropriate assumptions, we construct the solution uε that concentrates around any given isolated local minimum of V by applying the penalization method for the above equation. [ABSTRACT FROM AUTHOR]