Asymptotic behavior of positive solutions for a class of quasilinear elliptic equations in \(\mathbb{R}^2\) (Q2928383)

The authors are concerned with the study of asymptotic behavior of positive solutions to the equation NEWLINE\[NEWLINE -\Delta u-k \Delta (|u|^\alpha)|u|^{\alpha-2}u=h(u)-\lambda u NEWLINE\]NEWLINE in the plane. Here \(\alpha>1\), \(k\) is a positive real parameter. The authors study the asymptotic behavior of the ground state solution as \(k\to 0\). The uniqueness and the non-degeneracy of the ground state for small \(k\) is also achieved.