Ground states of a quasilinear equation (Q1328948)

The paper deals with the problem \(u'' - | u' |^ q + \lambda u^ p = 0\) on \(\mathbb{R}\), \(u \geq 0\), \(u \not \equiv 0\) on \(\mathbb{R}\), \(u(x) \to 0\) as \(x \to \pm \infty\), where the parameters \(\lambda\), \(p\) and \(q\) are positive. Some theorems are proved, studying the existence, uniqueness and asymptotic properties of the solutions of this problem for the following parameter values: \(0 < p < \infty\) and \(q < 2p/(p + 1)\).