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We deal with the boundary value problem $$\begin{array}{ccccccc}\hfill -\Delta u\left(x\right)& ={\lambda }_{1}u\left(x\right)+g\left(\nabla u\left(x\right)\right)+h\left(x\right),\hfill & & x\in \Omega u\left(x\right)\hfill & \hfill =0,& & \hfill x\in \partial \Omega \end{array}$$ where $\Omega \subset {ℝ}^N$ is an smooth bounded domain, ${\lambda }_1$ is the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary conditions on $\Omega$, $h\in L^{max\{2,N/2\}}\left(\Omega \right)$ and $g:{ℝ}^N⟶ℝ$ is bounded and continuous. Bifurcation theory is used as the right framework to show the existence of solution provided that $g$ satisfies certain conditions on the origin and at infinity.