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PreprintCC BY 4.0arXiv

A p-Laplacian Problem with Slightly Subcritical Regularly Varying Nonlinearity

  • Mabel Cuesta
  • Rosa Pardo
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Abstract

We study a quasilinear elliptic problem involving the p-laplacian operator and a slightly subcritical nonlinearity with a sign-changing weight. We assume that the slightly subcritical nonlinearity is a regularly varying function at zero and at infinity, which are not necessarily asymptotic to a power at infinity. We state sufficient conditions which guarantee a Palais-Smale condition. We also provide a bifurcation theorem for these nonlinearities, which allow us to state the existence of a bifurcated branch of positive solutions, containing a turning point, and multiplicity of solutions.

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Cite

BibTeXRIS
BibTeX
@misc{cuesta2026plaplacian,
  title = {{A $p$-Laplacian Problem with Slightly Subcritical Regularly Varying Nonlinearity}},
  author = {Mabel Cuesta and Rosa Pardo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38596},
  eprint = {2610.38596},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38596},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A p-Laplacian Problem with Slightly Subcritical Regularly Varying Nonlinearity
AU  - Mabel Cuesta
AU  - Rosa Pardo
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38596
UR  - https://arxiv.org/abs/2610.38596
AB  - We study a quasilinear elliptic problem involving the p-laplacian operator and a slightly subcritical nonlinearity with a sign-changing weight. We assume that the slightly subcritical nonlinearity is a regularly varying function at zero and at infinity, which are not necessarily asymptotic to a power at infinity. We state sufficient conditions which guarantee a Palais-Smale condition. We also provide a bifurcation theorem for these nonlinearities, which allow us to state the existence of a bifurcated branch of positive solutions, containing a turning point, and multiplicity of solutions.
ER  -