Existence of normalized solutions for the mixed fractional Laplacians equation with different types of potentials

This paper studies the existence of normalized solutions for nonlinear equations involving mixed fractional Laplacians with different orders: { ( − ∆ ) s 1 u +( − ∆ ) s 2 u + V ( x ) u = λu + | u | p − 2 u, x ∈ R d, ∫ R d | u | 2 dx = c 2, where 1 ≤ d < 2 s 1 s 2 s 2 − s 1, 0 < s 1 < s 2 < 1, 2 < p < 2 + 4 s 2 d and the potential V : R d → [ 0, + ∞ ) is a bounded and continuous function. This type of equation appears in many fields and has been increasingly attracting the attention of scientists in recent years due to its numerous and important applications. By using variational methods, we can prove that, when V satisfies four different assumptions, the minimization of the energy functional is achieved. Supplementary Material File (fang-2025.pdf) - Download - 347.45 KB Information & Authors Information Version history Copyright This work is licensed under a Non Exclusive No Reuse License.

Authors Metrics & Citations Metrics Article Usage 130views 150downloads Citations Download citation Xingling Fang, Xin Qiu, Zeng-Qi Ou, et al. Existence of normalized solutions for the mixed fractional Laplacians equation with different types of potentials. Authorea. 11 August 2025. DOI: https://doi.org/10.22541/au.175489827.71212663/v1 DOI: https://doi.org/10.22541/au.175489827.71212663/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.