Nodal solutions for logarithmic weighted N-laplacian problem with exponential nonlinearities

Abstract

In this article, we study the following problem

$$\begin{aligned} -div (\omega (x)|\nabla u|^{N-2} \nabla u) = \lambda \ f(x,u) \quad \text{ in } \quad B, \quad u=0 \quad \text{ on } \quad \partial B, \end{aligned}$$

where B is the unit ball in \(\mathbb {R^{N}}\), \(N\ge 2\) and w(x) a singular weight of logarithm type. The reaction source f(x, u) is a radial function with respect to x and is subcritical or critical with respect to a maximal growth of exponential type. By using the constrained minimization in Nehari set coupled with the quantitative deformation lemma and degree theory, we prove the existence of nodal solutions.