1/2-Laplacian problem with logarithmic and exponential nonlinearities

Chen, Zigao (2023) 1/2-Laplacian problem with logarithmic and exponential nonlinearities. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2023 (37). pp. 1-19. ISSN 1417-3875

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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.

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