Nodal solutions for Logarithmic weighted $N$-Laplacian problem with exponential nonlinearities

Abstract

In this article, we study the following problem $$-{\rm div} (ω(x)|\nabla u|^{N-2} \nabla u) = λ f(x,u) \quad\mbox{ in }\quad B, \quad u=0 \quad\mbox{ on } \quad\partial B,$$ where $B$ is the unit ball of ${\mathbb{R}}^{\mathbb{N}}$, $N\ge 2$ 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.

arXiv admin note: substantial text overlap with arXiv:2206.10001