Ground state solutions for weighted biharmonic Kirchhoff problem via the Nehari manifold approach

In this article, we delve into the investigation of the following non-local problem within the unit ball B1 of R4: g(∫B1wβ(x)|Δu|2)Δwβ2u=|u|q−2u+f(x,u)inB1,u=∂nu=0on∂B1,where Δwβ2.=Δ(wβ(x)Δ.) is the weighted Biharmonic operator, where wβ(x) represents a logarithmically singular weight, and the non-linearity involves a combination of a reaction source f(x,u), critical in the context of Adams' type exponential inequality and a polynomial function. The Kirchhoff function g is characterized by being positive and continuous. Employing the Nehari manifold method, the quantitative deformation lemma and degree theory results, we establish the existence of a ground state solution.