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In this work, we will prove the existence of bounded solutions for the nonlinear elliptic equations \(- div(a(x,u,\nabla u)) = g(x,u,\nabla u) -divf,\) in the setting of the weighted Sobolev space \(W^{1,p}(\Omega,w)\) where \(a\), \(g\) are Caratheodory functions which satisfy some conditions and \(f\) satisfies suitable summability assumption.