Existence of infinitely many distinct solutions to the quasirelativistic Hartree-Fock equations
Summary: We establish existence of infinitely many distinct solutions to the semilinear elliptic Hartree-Fock equations for \(N\)-electron Coulomb systems with quasirelativistic kinetic energy \(\sqrt{-\alpha^{-2}\Delta _{x_{n}}+\alpha ^{ - 4} - \alpha^{ - 2}}\) for the \(N\)th electron. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge \(Z_{\text{tot}}\) of \(K\) nuclei is greater than \(N - 1\) and that \(Z_{\text{tot}}\) is smaller than a critical charge \(Z_{c}\). The proofs are based on a new application of the Fang-Ghoussoub critical point approach to multiple solutions on a noncompact Riemannian manifold, in combination with density operator techniques.
scientific article; zbMATH DE number 5627900
scientific article