Super and subsolutions for elliptic equations on all of \(\mathbb R^n\)
Summary: By construction sub and supersolutions for the following semilinear elliptic equation \(-\Delta u(x)=\lambda g(x)f(u(x))\), \(x\in \mathbb R^n\) which arises in population genetics, we derive some results about the theory of existence of solutions as well as asymptotic properties of the solutions for every \(n\) and for the function \(g:\mathbb R^n\to \mathbb R\) such that \(g\) is smooth and is negative at infinity.
scientific article; zbMATH DE number 1821310