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<p>This paper investigates the existence of weak solutions for a class of singular Schrödinger-type elliptic systems driven by a generalized nonhomogeneous operator and involving Hardy-type potentials, together with nonlinear terms exhibiting critical growth in the sense of the Sobolev embedding and general growth conditions that do not satisfy the Ambrosetti-Rabinowitz condition. The presence of singular Hardy potentials, with the origin contained in the domain, combined with critical nonlinearities, leads to a serious loss of compactness. To overcome this difficulty, we establish a key result that allows the application of a Brezis-Lieb type lemma within the nonhomogeneous framework. By employing variational methods adapted to this general setting, we extend previous works by addressing a broader class of nonhomogeneous operators.</p>

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On the existence of weak solutions for nonhomogeneous elliptic system involving hardy potentials and critical nonlinearities

  • 期刊论文

  • 发表日期：

    2026年7月12日

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  • Abdelhak Mokhtari,
  • Brahim Bougherara

摘要

This paper investigates the existence of weak solutions for a class of singular Schrödinger-type elliptic systems driven by a generalized nonhomogeneous operator and involving Hardy-type potentials, together with nonlinear terms exhibiting critical growth in the sense of the Sobolev embedding and general growth conditions that do not satisfy the Ambrosetti-Rabinowitz condition. The presence of singular Hardy potentials, with the origin contained in the domain, combined with critical nonlinearities, leads to a serious loss of compactness. To overcome this difficulty, we establish a key result that allows the application of a Brezis-Lieb type lemma within the nonhomogeneous framework. By employing variational methods adapted to this general setting, we extend previous works by addressing a broader class of nonhomogeneous operators.