We consider the problem −( a+b∫RN|∇w|2dy)▵w + H(y)w = g(y,w), y∈RN where a,b > 0 and H( y) ∈ C (RN,R) is a sign-changing function. With a subquadratic growth g , the existence of multiple solutions of the Kirchhoff equation is proved. The (PS) condition is proved. And, we prove the functional J satisfies the local linking geometry and J is bounded from below. The problem has two nontrivial solutions by using the local linking theorem.
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