In this paper, we have conducted and investigated the existence of solutions for a fourth-order quasilinear elliptic equation. This equation incorporates a perturbed 1-biharmonic problem, represented as Δ 2 1 v = 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.
