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In this paper, we consider the existence of solutions of the following Kirchhoff-type problem \ \ array [c{ll - (a+bₑ℃| u|²dx) u+ V (x) u=f (x, u), ~in~ R^3, \\ u H¹ (R³), array. \] where a, b are postive constants, and the potential V (x) is continuous and indefinite in sign. Under some suitable assumptions on V (x) and f, we obtain the existence of solutions by the Symmetric Mountain Pass Theorem.
Xiao et al. (Thu,) studied this question.