{
  "abstract": "This paper is devoted to the study of a nonlinear boundary value problem driven by a combination of mixed variable-exponent triharmonic operators and a Hardy-type singular potential. Specifically, we consider \\[ \\begin{cases} -a(x)\\,Δ_{p(x)}^{3}u - b(x)\\,Δ_{q(x)}^{3}u + m(x)\\,\\dfrac{|u|^{s(x)-2}u}{|x|^{3s(x)}} = μf(x,u), & \\text{in } Ω, \\\\ u = Δu = Δ^{2}u = 0, & \\text{on } \\partialΩ, \\end{cases} \\] where $Ω\\subset \\mathbb{R}^N$ is a smooth bounded domain with $N > 3$. The operators $Δ_{p(x)}^{3}$ and $Δ_{q(x)}^{3}$ represent triharmonic operators with variable exponents, creating a framework of nonstandard growth. Under suitable assumptions on the variable exponents $p(x), q(x), s(x)$, the weight functions $a(x), b(x), m(x)$, and the nonlinearity $f(x,u)$, we establish the existence of at least three distinct weak solutions. Our approach is variational, relying on critical point theory for functionals defined on variable-exponent Sobolev spaces. By combining Ricceri's and Bonanno-Marano's abstract three critical points theorems with new Hardy-Rellich inequalities adapted to the variable-exponent setting, we prove our main multiplicity result for small values of the parameter $μ$. To our knowledge, this work presents the first systematic treatment of sixth-order problems featuring simultaneously mixed variable exponents and Hardy-type singular potentials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33576",
  "author_total": 3,
  "authors": [
    {
      "name": "Khalid Soualhine"
    },
    {
      "name": "Adnane Belakhdar"
    },
    {
      "name": "Mohamed karim Hamdani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fq0py2xk2pg1b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33576",
  "fulltext_url": null,
  "id": "fq0py2xk2pg1b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33576",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.33576",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fq0py2xk2pg1b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33576",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33576"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Multiplicity of weak solutions for mixed variable exponent triharmonic problems with hardy potentials",
  "title_text": "Multiplicity of weak solutions for mixed variable exponent triharmonic problems with hardy potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/fq0py2xk2pg1b",
  "venue": "arXiv",
  "versions": []
}