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<p>In this paper, we establish continuous and compact embedding results for a class of weighted Sobolev spaces with variable exponents in unbounded domains. By leveraging these embedding results and an abstract critical point theorem, we prove the existence and multiplicity of weak solutions for degenerate weighted quasilinear elliptic equations involving nonlocal nonlinearities and variable exponents.</p>

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Degenerate weighted quasilinear elliptic equations with nonlocal terms: existence and multiplicity of weak solutions in \(\mathbb {R}^{N}\)

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Khaled Kefi,
  • Anouar Bahrouni

摘要

In this paper, we establish continuous and compact embedding results for a class of weighted Sobolev spaces with variable exponents in unbounded domains. By leveraging these embedding results and an abstract critical point theorem, we prove the existence and multiplicity of weak solutions for degenerate weighted quasilinear elliptic equations involving nonlocal nonlinearities and variable exponents.