Existence of Signed and Sign-Changing Solutions for Weighted Kirchhoff Problems with Critical Exponential Growth

Abstract

This work is devoted to study the existence of least energy sign-changing solutions for a nonlocal weighted Schrödinger-Kirchhoff 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.