Abstract We consider quasilinear Schrödinger equations in RN of the form - u+V (x) u-u (u²) =g (u), where the potential V is allowed to be sign-changing and the nonlinearity g is sublinear at zero. Except for being subcritical, no additional condition is imposed on g (u) for |u| large. We obtain a sequence of solutions with negative energy and converging to zero via Clark’s theorem. We also obtain a similar result for fourth-order quasilinear Schrödinger equations in RN of the form ²u- u+ V (x) u-u (u²) =g (u).
Shen et al. (Mon,) studied this question.
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