Skip to content
DraconiticResearch
Search Sources API
181,716 studies31 sourcesUpdated 32 min ago
Peer-reviewedCC BY 4.0Mathematics

Normalized Solutions for a Class of the Nonlinear Elliptic Systems with Mixed-Power Nonlinearities on Bounded Domains

  • Liang Zhang1
  • Juan Liu1
  • Jing Shao1
  • Qingzhe Wu1
  1. 1College of Sciences, Shenyang University, Shenyang 110044, China
Open at sourceDOICite

Abstract

In this paper, we discuss the existence of normalized solutions for a class of the nonlinear elliptic systems with mixed-power nonlinearities on bounded domains. When the lower-order nonlinearity is L2-subcritical and the leading term is L2-critical, the global solutions can be found by minimum principle. If the lower-order nonlinearity is L2-subcritical or L2-critical and the leading term is L2-supercritical and Sobolev-subcritical, we can find the local minimum solutions by providing some proper conditions about the parameters. Furthermore, if the lower-order nonlinearity is L2-critical and the leading term is Sobolev-critical, we restore the compactness of a minimizing sequence so that the local solution can be achieved.

Related

  1. Infinitely many normalized solutions of L2-supercritical NLS equations on noncompact metric graphs with localized nonlinearities
    Pablo Carrillo, Damien Galant, Louis Jeanjean +1
    Discrete and Continuous Dynamical Systems - Series APeer-reviewedCC BY 4.0Full text2 citedAnalysis & PDEsHAL
  2. Existence of infinitely many solutions for nonlinear Poisson-Poisson elliptic systems
    Raul Nina-Mollisaca, Julio Huayta-Centeno, Mauricio Sepulveda-Cortes +1
    Electronic Journal of Differential EquationsPeer-reviewedCC BYFull textGeneral mathematicsDOAJ
  3. Existence and non-existence of nonradial solutions to an elliptic equation on hyperbolic space with critical and subcritical nonlinearities
    Atanu Manna, Bhakti Bhusan Manna
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. Interior Regularity for Stable Solutions of Semilinear Elliptic Equations with Sign-Changing Nonlinearities
    Long-Han Huang, Yuxuan Zhou, Wenming Zou
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Anisotropic quasilinear elliptic systems involving nonlinearities with negative critical terms
    Elisandra Gloss, Artur Jorge Marinho, Kanishka Perera
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@article{zhang2026normalized,
  title = {{Normalized Solutions for a Class of the Nonlinear Elliptic Systems with Mixed-Power Nonlinearities on Bounded Domains}},
  author = {Liang Zhang and Juan Liu and Jing Shao and Qingzhe Wu},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213905},
  url = {https://www.mdpi.com/2227-7390/14/21/3905},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Normalized Solutions for a Class of the Nonlinear Elliptic Systems with Mixed-Power Nonlinearities on Bounded Domains
AU  - Liang Zhang
AU  - Juan Liu
AU  - Jing Shao
AU  - Qingzhe Wu
PY  - 2026
DA  - 2026/10/26
JO  - Mathematics
DO  - 10.3390/math14213905
UR  - https://www.mdpi.com/2227-7390/14/21/3905
AB  - In this paper, we discuss the existence of normalized solutions for a class of the nonlinear elliptic systems with mixed-power nonlinearities on bounded domains. When the lower-order nonlinearity is L2-subcritical and the leading term is L2-critical, the global solutions can be found by minimum principle. If the lower-order nonlinearity is L2-subcritical or L2-critical and the leading term is L2-supercritical and Sobolev-subcritical, we can find the local minimum solutions by providing some proper conditions about the parameters. Furthermore, if the lower-order nonlinearity is L2-critical and the leading term is Sobolev-critical, we restore the compactness of a minimizing sequence so that the local solution can be achieved.
SN  - 2227-7390
ER  -