Asymptotic results for finite energy solutions of semilinear elliptic equations
The author studies nonnegative (weak) solutions \(u:\mathbb{R}^ n\to\mathbb{R}\), \(n\geq 3\), of differential inequalities of the principal form \(\Delta u+f(x,u)\geq 0\) which is required to hold only for large values of \(| x|\). The nonlinearity \(f\) is radial in the space variable and has to satisfy certain sign and growth properties. It is shown that \(\limsup_{x\to\infty}u(x)| x|^{n-2}<\infty\) holds provided \(u\) is of finite energy. Further results contain a more careful description of this asymptotic behaviour.
scientific article; zbMATH DE number 40244
scientific article