Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations
The authors study the non-autonomous Choquard-Pekar equation: \[-\vartriangle u + V(x)u = (W *F(u))f(u), \quad x \in \mathbb R^N (N \geq 2), \; u \in H^1(\mathbb R^N),\] where the potential \(V(x)\) is 1-periodic and 0 lies in a gap of the spectrum of the Schrödinger operator \(- \vartriangle + \, V\). Under some general assumptions concerning the potential \(W\) and the nonlinearity \(f\), they prove the existence of ground state solutions. They also construct infinitely many geometrically distinct solutions by using variational methods and deformation arguments.
scientific article; zbMATH DE number 7291353
scientific article