Abstract
<abstract> In the paper, we investigate a class of Schrödinger equations with sign-changing potentials $ V(x) $ and sublinear nonlinearities. We remove the coercive condition on $ V(x) $ usually required in the existing literature and also weaken the conditions on nonlinearities. By proving a Hardy-type inequality, extending the results in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, and using it together with variational methods, we get at least one or infinitely many small energy solutions for the problem. </abstract>
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