On the asymptotics of ground states for a boundary value problem for the equation $-\epsilon {\Delta }_{p}u=a|u{|}^{q-2}u-b|u{|}^{\gamma -2}u$

Yavdat Sh. Il'yasov, Elvira I. Turianova

We study a singularly perturbed Dirichlet problem for the $p$-Laplacian with competing superlinear terms, \[ -\varepsilon Δ_p u = a(x)|u|^{q-2}u - b(x)|u|^{γ-2}u, \qquad u|_{\parti…