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This paper studies the multiplicity of solutions for the fourth-order boundary value problem at resonance with variable coefficients $$displaylines{ u^{(4)}+eta(t)u''-lambda_1u=g(t, u)+h(t),quad tin(0, 1),cr u(0)=u(1)=u''(0)=u''(1)=0, }$$ where $etain C[0,1]$ with $eta(t)<pi^2$ on $[0,1]$, $g:[0, 1]imes mathbb{R}o mathbb{R}$ is bounded continuous function, $hin L^2(0,1)$ and $lambda_1>0$ is the first eigenvalue of the associated linear homogeneous boundary value problem $$displaylines{ u^{(4)}+eta(t)u''-lambda u=0,quad tin(0, 1),cr u(0)=u(1)=u''(0)=u''(1)=0. }$$ The proof of our main result is based on the connectivity properties of the solution sets of parameterized families of compact vector fields.