${1 / 2}$-Laplacian problem with logarithmic and exponential nonlinearities

Abstract

In this paper, based on a suitable fractional Trudinger–Moser inequality, we establish sufficient conditions for the existence result of least energy sign-changing solution for a class of one-dimensional nonlocal equations involving logarithmic and exponential nonlinearities. By using a main tool of constrained minimization in Nehari manifold and a quantitative deformation lemma, we consider both subcritical and critical exponential growths. This work can be regarded as the complement for some results of the literature.

Keywords

• $1 / 2$-laplacian operator
• logarithmic nonlinearity
• exponential nonlinearity
• sign-changing solutions