(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
We consider the biharmonic equation ∆^2u− (a+b_R^5 |∇u|^2 dx) ∆u + V (x)u = f(u), where V(x) and f(u) are continuous functions. By using a perturbation approach and the symmetric mountain pass theorem, the existence and multiplicity of solutions for this equation are obtained, and the power-type case f(u) = |u|^ p−2u is extended to p ∈ (2, 10), where it was assumed p ∈ (4, 10) in many papers.