Work

Normalized solutions to a class of (2, q )-Laplacian equations

Year: 2025

Type: article

Abstract: 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 $ \overrightarrow {a}\left(\xi \right)=\vert \xi {\vert }^{q-2}\xi $ 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.

Source: Advanced Nonlinear Studies

DOI: 10.1515/ans-2023-0163

Authors: Laura Baldelli, Tao Yang

Institutions: Universidad de Granada, Zhejiang Normal University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,469

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", National Natural Science Foundation of China, Narodowym Centrum Nauki, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni