Abstract
We apply the Pohozaev identity to show the nonexistence of nontrivial solutions to a semilinear equation of the form (H−E)u=f(x,∣u∣)u, where E is a real constant lying on the essential spectrum of H. The self-adjoint operators H under consideration are the Schrödinger operator with Coulomb-type potentials, the Stark-like Hamiltonian, and the semirelativistic Hamiltonian.
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