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<p>In this paper, we study the existence and the multiplicity of solutions for a coupled elliptic system defined in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^4\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation>. Initially, we provide a reformulation of the system and conduct an analysis of the Palais-Smale sequence. Following this, we prove the existence of a ground state solution. This leads to the establishment of a compactness result, which sets the stage for an exploration of the multiplicity of solutions through the application of the Ljusternik-Schnirelmann category and variational techniques.</p>

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Multiplicity of solutions for Kirchhoff-Boussinesq systems with exponential growth

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • A. Razani,
  • R. Carlos,
  • S. Salirrosas

摘要

In this paper, we study the existence and the multiplicity of solutions for a coupled elliptic system defined in \(\mathbb {R}^4\) R 4 . Initially, we provide a reformulation of the system and conduct an analysis of the Palais-Smale sequence. Following this, we prove the existence of a ground state solution. This leads to the establishment of a compactness result, which sets the stage for an exploration of the multiplicity of solutions through the application of the Ljusternik-Schnirelmann category and variational techniques.