Symmetric and nonsymmetric solutions for an elliptic equation on \(\mathbb R^N\)
The authors establish the existence of a positive solution, as well as that of nonradial solutions, which changes sign, for nonlinear elliptic problem \[ -\Delta u+V(z)u=f(z,u)\quad u\in H^1(\mathbb R^N),\tag{1} \] where \(V:\mathbb R^N\to\mathbb R\) is a given non-negative potential and \(f\), \(f:\mathbb R^N\times\mathbb R\to\mathbb R\) is a Hölder continuous function. Under some additional assumptions on \(V\) and \(f\), the authors show that the problem (1) has two nontrivial solutions.
scientific article; zbMATH DE number 2105457