Some remarks on the supersolution-subsolution method for superlinear elliptic equations
The authors study the equation \(\Delta u+K(x)u^ p=0\), where \(x\in {\mathbb{R}}^ n\), \(n\geq 3\), \(p>1\), and K is positive. They show that it is in general impossible to prove the existence of a non-trivial solution to this equation by an effective construction of sub- and supersolutions since if v and w, \(0\leq v\leq w\), are sub- and supersolution, respectively, then, under suitable decay hypothesis on K and W it follows already that \(v=w\) is a solution. This theorem is based on a second result in the paper which says that under corresponding hypotheses any nonnegative subsolution is \(O(| x|^{2-n})\) for \(| x| \to \infty\).
scientific article; zbMATH DE number 4027985
scientific article