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Infinitely many solutions for a class of sublinear Schr\"{o}dinger equations
Keywords:Sublinear Schr\"{o}dinger equation, local sublinear nonlinearities, symmetric mountain lemma, variational methods.
      In this paper, we investigate the Schr\"{o}dinger equation, which satisfies that the potential is asymptotical 0 at infinity in some measure-theoretic and the nonlinearity is sublinear growth. By using variant symmetric mountain lemma, we obtain infinitely many solutions for the problem. Moreover, if the nonlinearity is locally sublinear defined for $|u|$ small, we can also get the same result. In which, we show that these solutions tend to zero in $L^{\infty}(\mathbb{R}^{N})$ by the Br\''{e}zis-Kato estimate.