Ground state solutions for weighted fourth-order Kirchhoff problem via Nehari method

In this article, we study the following non local problem $$g({\int }_{B}w(x)\mathrm{\mid }\mathrm{\Delta }u{\mathrm{\mid }}^2)\mathrm{\Delta }(w(x)\mathrm{\Delta }u)=\mathrm{\mid }u{\mathrm{\mid }}^{q-2}u+f(x,u)inB,u=\frac{\mathrm{\partial }u}{\mathrm{\partial }n}=0on\mathrm{\partial }B,$$ where $B$ is the unit ball in ${\mathbb{R}}^4$ and $w(x)$ is a singular weight of logarithm type. The non-linearity is a combination of a reaction source $f(x,u)$ which is critical in view of exponential inequality of Adams’ type and a polynomial function. The Kirchhoff function $g$ is positive and continuous. By using the Nehari manifold method , the quantitative deformation lemma and degree theory results, we establish the existence of a ground state solution.