Skip to content
DraconiticResearch
Search Sources API
189,273 studies31 sourcesUpdated 45 min ago
Peer-reviewedCC BY 4.0Axioms

Existence Results for the Critical Biharmonic Elliptic Equation Involving Singular Nonlinearities

  • Xun Yang1
  • Xaychalern Kongkeo2
  • Guaiqi Tian1
  1. 1School of Sciences, Guizhou University of Engineering Science, Bijie 551700, China
  2. 2Confucius Institute, Faculty of Languages, Souphanouvong University, Luang Prabang 06000, Laos
Open at sourceDOICite

Abstract

The present work is concerned with a class of biharmonic elliptic equations involving critical and singular nonlinearities. Under the assumption that p(x) attains its global maximum at some point, we derive that the problem admits a mountain pass type solution via the Brezis-Lieb lemma. Meanwhile, if p(x) has k global maximum points, we establish the existence of k nontrivial solutions by virtue of variational methods and the Nehari manifold.

Related

  1. Existence of solutions for a nonlinear elliptic equation involving (p(x),q(x))-Laplacian and (p(x),q(x))-biharmonic Operator
    Zehra Yücedağ, Enver Ferhan
    Cumhuriyet Science JournalPeer-reviewedCC BY-NCFull textGeneral mathematicsDOAJ
  2. Anisotropic quasilinear elliptic systems involving nonlinearities with negative critical terms
    Elisandra Gloss, Artur Jorge Marinho, Kanishka Perera
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  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. A class of degenerate elliptic problems involving the Grushin operator: critical mass and ground states
    Aleks Jevnikar, Senli Liu, Yu Su
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Existence and Asymptotic Behavior of Normalized Ground States for a Weighted Elliptic System with Caffarelli--Kohn--Nirenberg Critical Exponent
    Asmita Rai, Divya Goel
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@article{yang2026existence,
  title = {{Existence Results for the Critical Biharmonic Elliptic Equation Involving Singular Nonlinearities}},
  author = {Xun Yang and Xaychalern Kongkeo and Guaiqi Tian},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15110804},
  url = {https://www.mdpi.com/2075-1680/15/11/804},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Existence Results for the Critical Biharmonic Elliptic Equation Involving Singular Nonlinearities
AU  - Xun Yang
AU  - Xaychalern Kongkeo
AU  - Guaiqi Tian
PY  - 2026
DA  - 2026/10/29
JO  - Axioms
DO  - 10.3390/axioms15110804
UR  - https://www.mdpi.com/2075-1680/15/11/804
AB  - The present work is concerned with a class of biharmonic elliptic equations involving critical and singular nonlinearities. Under the assumption that p(x) attains its global maximum at some point, we derive that the problem admits a mountain pass type solution via the Brezis-Lieb lemma. Meanwhile, if p(x) has k global maximum points, we establish the existence of k nontrivial solutions by virtue of variational methods and the Nehari manifold.
SN  - 2075-1680
ER  -