Positive singular solutions for semilinear elliptic equations with supercritical growth
The main part of the paper deals with positive, singular and radially symmetric solutions of the problem \(\Delta u+ f(u)=0\). The author shows that there exists a solution \(U(r)\) tending to \(\infty\) as \(r=| x|\to 0\) if \(f(u)\in C^ 1 (\mathbb{R})\) is supercritical at \(u=+ \infty\), and further \(U(r)\) has a finite zero if \(f(u)\) is positive for \(u>0\) and satisfies a certain subcritical condition at \(u=0\). The proof is based on a Pohozaev identity and usual ODE arguments.
positive, singular and radially symmetric solutions
scientific article; zbMATH DE number 696880