On the cubic-quintic Schrödinger equation Baldelli, Laura This paper explores the cubic-quintic Schrödinger equation in the entire Euclidean space. Our objectives are twofold: first, to advance the understanding of unresolved issues related to this equation, which are well known in the extensively studied Gross-Pitaevskii equation. Second, to consolidate existing results on the cubic-quintic equation, providing partial contributions. Specifically, we determine the explicit constant for the a priori bound and establish a partial existence result for finite energy traveling waves in suitable approximate domains of R d. 2025-07-31T09:03:47Z 2025-07-31T09:03:47Z 2025-07-30 journal article Baldelli, L. On the cubic-quintic Schrödinger equation. Nonlinear Differ. Equ. Appl. 32, 105 (2025). [https://doi.org/10.1007/s00030-025-01109-8] https://hdl.handle.net/10481/105883 https://doi.org/10.1007/s00030-025-01109-8 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Springer Nature