Abstract
In this paper, we prove the existence of nontrivial solutions for perturbed Schrödinger systems with pinching and mixed nonlinearities, where the nonlinearities are composed of sublinear terms, asymptotically linear terms (pinching terms) and superlinear terms. When the system is time-independent and perturbed, we obtain the existence of nontrivial homoclinic solutions. When the system is time-dependent and non-perturbed, we obtain the existence of nontrivial standing waves and homoclinic solutions. In addition, we also give some function examples that are suitable for our models.