Positive solutions of a semilinear elliptic equation and its asymptotic behaviour (Q1177297)

The author establishes the existence of positive solutions for semilinear elliptic problems \[ -\Delta u=\lambda f(u-a) \text{ in } \mathbb{R}^ N,\;u(x) \to 0 \text{ and } | \nabla u(x) | \to 0 \text{ as } | x | \to \infty, \tag{P} \] where \(f\) is ``superlinear'' at infinity, \(\lambda\) and \(a\) are positive constants; moreover, we investigate the limiting behaviour of solutions of (P) as \(\lambda\) and \(a\) are taken as parameters.