Asymptotical behavior of solutions of nonlinear elliptic equations in \(\mathbb{R}^N\) (Q1598242)

The present paper is devoted to study nonnegative solutions of the semilinear elliptic equation with non-Lipschitzian nonlinearity \[ -\Delta u+ u^q-u^p=0, \tag{1} \] with \(q\in(0,1)\) and \(p>q\). The authors address to following question: Letting \(u\in C^2(\mathbb{R}^N)\) be a nonnegative solution of equation (1) in \(\mathbb{R}^N\), with \(N\geq 2\), one can describe the precise behaviour of \(u\) near infinity. The authors give a complete classification of solutions of (1).