Abstract In this paper, we consider a boundary problem for a p -biharmonic equation Δ Δ u p − 2 Δ u = a x u p − 2 u ln u + b x u p − 2 u ({u }^p-2u) =a (x) u ^p-2uln u +b (x) u ^p-2u with a sign-changing logarithmic nonlinearity a x u p − 2 u ln u a (x) u ^p-2uln u and a polynomial nonlinearity b x u p − 2 u b (x) u ^p-2u in a bounded domain. We derive a new result regarding the existence of solutions and illustrate how the weight functions a x a (x) and b x b (x) can affect the existence and multiplicity of solutions. Furthermore, the sign-changing weight function a x <jats: tex-mat
Feng et al. (Thu,) studied this question.