Existence of solutions to a class of asymptotically linear Schrödinger equations in RnRn via the Pohozaev manifold

In this study, we investigate the nonexistence of a least energy solution and the existence of a positive solution for a class of nonhomogeneous asymptotically linear Schrödinger equations in RnRn via the Pohozaev manifold. After changing the variables, the quasilinear operator becomes a semilinear nonhomogeneous operator. The technique used employs variational methods that are constrained to the Pohozaev manifold, which are combined with the splitting lemma.