Solutions for ground states in weighted N2‐biharmonic Kirchhoff problem with nonlinear critical exponential growth

This paper investigates a fourth‐order weighted equation represented as where denotes the unit ball in and is a singular logarithmic weight. The nonlinearity in the equation comprises a reaction source takes the form of a radial function and plays a crucial role in the context of Adams' type exponential inequality and a polynomial function. The Kirchhoff function is positive and continuous. The proof of the existence result utilizes constrained minimization within the Nehari set, supplemented by the application of the quantitative deformation lemma and degree theory results.