Positive solution to \(p\)-Laplacian type scalar field equation in \(\mathbb{R}^N\) with nonlinearity asymptotic to \(u^{p-1}\) at infinity (Q2711950)

This paper is devoted to the existence of a positive solution to the following nonautonomous quasilinear scalar field equation: NEWLINE\[NEWLINE\begin{cases} -\text{div} \bigl( |\nabla u|^{p-2} \nabla u\bigr)+ m|u|^{p-2}u=f (x,u) \text{ in }\mathbb{R}^N \\ u\in W^{1,p}(\mathbb{R}^N),\;N>p>1\end{cases}. \tag{1}NEWLINE\]NEWLINE Moreover, if \(f(x,u) \equiv f(u)\), the existence of a ground state to (1) is also proved by using the artificial constraint method.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00021].