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<p>We investigate a class of nonlinear Schrödinger equations involving the biharmonic operator. Using variational methods, we establish the existence of least energy solutions (ground states) and prove their exponential decay at infinity. In particular, we show the existence of radially symmetric ground states for nonlinearities with both subcritical and critical Sobolev growth. The higher-order nature of the problem introduces significant technical challenges, which we address via refined variational techniques, including arguments inspired by Brézis and Lieb.</p>

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Least Energy Solutions and Exponential Decay for a Class of Fourth-Order Equations in Entire Space

  • 期刊论文

  • 发表日期：

    2025年12月2日

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  • João Marcos do Ó,
  • Antônio de Souza Filho,
  • José Francisco de Oliveira

摘要

We investigate a class of nonlinear Schrödinger equations involving the biharmonic operator. Using variational methods, we establish the existence of least energy solutions (ground states) and prove their exponential decay at infinity. In particular, we show the existence of radially symmetric ground states for nonlinearities with both subcritical and critical Sobolev growth. The higher-order nature of the problem introduces significant technical challenges, which we address via refined variational techniques, including arguments inspired by Brézis and Lieb.