In this paper, we have conducted and investigated the existence of solutions for a fourthorder quasilinear elliptic equation. This equation incorporates a perturbed 1-biharmonic problem, represented as Δ2 1v = g(x, v)+h(x). To achieve this, we established two distinct sets of assumptions for the function g and demonstrated that each set of conditions yields solutions with unique characteristics. Our approach is based on variational method
