Nodal solutions for Logarithmic weighted $(N,p)$-Laplacian problem with exponential nonlinearities

The main purpose of this paper is to study the existence of least energy sign-changing solutions for Logarithmic weighted $(N,p)$-Laplacian problem in the unit ball $B$ of ${\mathbb{R}}^N,$ $N>2$. The non-linearity of the equation is assumed to have exponential growth in view of Trudinger-Moser type inequalities. In order to obtain our existence result, we use the constrained minimization in Nehari set, the quantitative deformation Lemma and degree theory results.