2022/12/30 by Laura Baldelli, Tao Yang, Baldelli, Laura +1 · 1 citation
Mathematics · #35A15 #35B38 #35B40 #35J20 #35J60 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2212.14873
openalex publication_date 2022/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper concerns the existence of normalized solutions to a class of (2,q)-Laplacian equations in all the possible cases according to the value of p with respect to the critical exponent 2(1+2/N). In the L2-subcritical case, we study a global minimization problem and obtain a ground state solution. While in the L2-critical case, we prove several nonexistence results, extended also in the Lq-critical case. At last, we derive a ground state and infinitely many radial solutions in the L2-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-2ξ 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.