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<p>We study the existence of nonnegative solutions for indefinite Caffarelli-Kohn-Nirenberg type systems in both subcritical and critical cases. Using variational methods, we establish the existence of solutions by analyzing associated energy functionals. In both the subcritical and critical cases compactness arguments, Mountain Pass techniques and concentration-compactness principles (such as Brezis-Lieb Lemma) are employed to address the lack of compactness. Our results extend previous findings and provide new insights into the structure of solutions for such systems.</p>

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Existence results for nonnegative solutions of weighted quasilinear systems including subcritical and critical growths

  • 期刊论文

  • 发表日期：

    2025年7月10日

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  • Abdolrahman Razani,
  • Sami Baraket

摘要

We study the existence of nonnegative solutions for indefinite Caffarelli-Kohn-Nirenberg type systems in both subcritical and critical cases. Using variational methods, we establish the existence of solutions by analyzing associated energy functionals. In both the subcritical and critical cases compactness arguments, Mountain Pass techniques and concentration-compactness principles (such as Brezis-Lieb Lemma) are employed to address the lack of compactness. Our results extend previous findings and provide new insights into the structure of solutions for such systems.