Ground state solutions for a Kirchhoff type equation involving p-biharmonic operator with exponential growth non-linearity

In this article, we study the following non local weighted problem g (₁ (w (x) | u|^N{2}) dx) (w (x) | u|^N{2-2} u) =|u|^q-2u +\ f (x, u) in B, u= u n=0 on B, where B is the unit ball in R^N 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. The energy function loses compactness in the critical case. To remedy this, we introduce a new asymptotic condition for non-linearity and go through an intermediate problem. Using the Nehari manifold method, the quantitative deformation lemma and results from degree theory, we establish the existence of a ground-state solution.