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<p>In this paper, we prove a blow-up result for a nonlocal Klein-Gordon equation with a nonlocal Choquard nonlinearity. Additionally, we prove the instability of the ground state solution of the elliptic problem associated with the equation. To prove the blow-up and instability result, using the Pohozaev manifold, we give a new characterization of the ground state level. Finally, we also show a global existence result.</p>

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Blow Up for Nonlocal Klein-Gordon Equation with Choquard Nonlinearity

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Paulo Cesar Carrião,
  • André Vicente

摘要

In this paper, we prove a blow-up result for a nonlocal Klein-Gordon equation with a nonlocal Choquard nonlinearity. Additionally, we prove the instability of the ground state solution of the elliptic problem associated with the equation. To prove the blow-up and instability result, using the Pohozaev manifold, we give a new characterization of the ground state level. Finally, we also show a global existence result.