Least energy nodal solutions for a weighted ( N , p ) $(N, p)$ -Schrödinger problem involving a continuous potential under exponential growth nonlinearity

Abstract

Abstract This article aims to investigate the existence of nontrivial solutions with minimal energy for a logarithmic weighted ( N , p ) $(N,p)$ -Laplacian problem in the unit ball B of R N $\mathbb{R}^{N}$ , N > 2 $N>2$ . The nonlinearities of the equation are critical or subcritical growth, which is motivated by weighted Trudinger–Moser type inequalities. Our approach is based on constrained minimization within the Nehari set, the quantitative deformation lemma, and degree theory results.

Keywords

• ( N , p ) $(N,p)$ -Laplacian
• Moser–Trudinger’s inequality
• Nonlinearity of exponential growth
• Sign-changing solutions
• Quantitative deformation lemma
• Degree theory