Normalized solutions to a class of (2, q)-Laplacian equations Baldelli, Laura Yang, Tao (2, q)-Laplacian normalized solutions ground state solutions This paper is concerned with the existence of normalized solutions to a class of (2, q)-Laplacian equations in all the possible cases with respect to the mass critical exponents 2(1 + 2/N), q(1 + 2/N). In the mass subcritical cases, we study a global minimization problem and obtain a ground state solution. While in the mass critical cases, we prove several nonexistence results. At last, we derive a ground state and infinitely many radial solutions in the mass supercritical case. Compared with the classical Schrödinger equation, the (2, q)-Laplacian equation possesses a quasi-linear term, which brings in some new difficulties and requires a more subtle analysis technique. Moreover, the vector field → a ( ξ ) = | ξ | q − 2 ξ corresponding to the q-Laplacian is not strictly monotone when q < 2, so we shall consider separately the case q < 2 and the case q > 2. 2025-02-27T08:12:58Z 2025-02-27T08:12:58Z 2025-02-07 journal article Baldelli, L. & Yang, T. (2025). Normalized solutions to a class of (2, q)-Laplacian equations. Advanced Nonlinear Studies, 25(1), 225-256. https://doi.org/10.1515/ans-2023-0163 https://hdl.handle.net/10481/102757 10.1515/ans-2023-0163 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional De Gruyter