Skip to content
DraconiticResearch
Search Sources API
189,105 studies31 sourcesUpdated 14 min ago
PreprintCC BY-NC-ND 4.0arXiv

Existence of positive solutions to anisotropic elliptic equations in the entire Euclidean space

  • Rulong Xie
  • Hailian Wang
  • Lei Yang
Open at sourcePDFDOICite

Abstract

In this paper, we research an anisotropic elliptic equation in the entire Euclidean space R^{N} . Under the assumption that the nonlinearity of the equation has exponential or critical growth, we prove, by means of the mountain-pass theorem, that the equation admits a nontrivial positive weak solution. Moreover, applying the mountain-pass theorem and Ekeland's variational principle, we show that a perturbation of the equation possesses two distinct positive weak solutions.

Related

  1. Existence, multiplicity and asymptotic behavior of positive solutions to (p,q)-Laplacian elliptic systems
    Xiankui Meng, Meiqiang Feng
    Electronic Journal of Differential EquationsPeer-reviewedCC BYFull textGeneral mathematicsDOAJ
  2. A sufficient condition for the existence of solutions of singular linear-quadratic vector equations
    Rishikesh Yadav, Axel Flinth
    arXivPreprintCC BY-SA 4.0Full textNumerical analysis & scientific computingarXiv
  3. Existence of positive Solutions to Hénon equation on integer Lattice graph and Half-Space
    Huyuan Chen, Lixun Jia
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Rigidity results via a Poincaré type formula for stable solutions of quasilinear anisotropic elliptic equations
    Berardino Sciunzi, Domenico Vuono
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Lyapunov-Krasovsky Functionals and the Existence of Unbounded Solutions of Functional-Differential Equations of Retarded Type
    Lapin K. S., Lapin S. V
    arXivPreprintarXiv licenceFull textAnalysis & PDEsDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{xie2026existence,
  title = {{Existence of positive solutions to anisotropic elliptic equations in the entire Euclidean space}},
  author = {Rulong Xie and Hailian Wang and Lei Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17601},
  eprint = {2610.17601},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17601},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Existence of positive solutions to anisotropic elliptic equations in the entire Euclidean space
AU  - Rulong Xie
AU  - Hailian Wang
AU  - Lei Yang
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17601
UR  - https://arxiv.org/abs/2610.17601
AB  - In this paper, we research an anisotropic elliptic equation in the entire Euclidean space R^{N} . Under the assumption that the nonlinearity of the equation has exponential or critical growth, we prove, by means of the mountain-pass theorem, that the equation admits a nontrivial positive weak solution. Moreover, applying the mountain-pass theorem and Ekeland's variational principle, we show that a perturbation of the equation possesses two distinct positive weak solutions.
ER  -