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Abstract In this paper, we study the following biharmonic equation: {Δ2u−Δu+λV(x)u=α(x)f(u)+μK(x)|u|q−2uin RN,u∈H2(RN), $$ \textstyle\begin{cases} \Delta^{2}u - \Delta u + \lambda V( x)u = \alpha( x) f(u) + \mu K(x) \vert u \vert ^{q-2}u \quad\text{in } \mathbb{R}^{N},\\ u\in H^{2}(\mathbb{R}^{N}), \end{cases} $$ where Δ2u=Δ(Δu) $\Delta^{2}u=\Delta(\Delta u)$, N>4 $N>4$, λ>0 $\lambda>0$, 1<q<2 $1< q<2$ and μ∈[0,μ0] $\mu\in[0,\mu_{0}]$. By using Ekeland’s variational principle and Gigliardo–Nirenberg’s inequality, we prove the existence of nontrivial solution for the above problem.