Least energy sign-changing solution for N-Laplacian problem with logarithmic and exponential nonlinearities

Abstract

In this paper, we establish sufficient conditions for the existence result of least energy sign-changing weak solution to the following quasilinear nonhomogeneous N-Laplacian equation with logarithmic and exponential nonlinearities:{−ΔNu=|u|p−2uln⁡|u|2+μf(u),inΩ,u=0,on∂Ω, where f(t) behaves like eα|t|N/(N−1). By using a main tool of constrained minimization in Nehari manifold, we consider both subcritical and critical exponential growths.