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<p>In this work, we mainly study a weighted fourth-order problem in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ 𝕉^{4} $</EquationSource> </InlineEquation>.According to the Adams-type inequalities,we assume the nonlinearity to have a critical or subcritical exponential growth.We establish the existence of a weak solution to this problem by usingthe mountain pass theorem.The major difficulty in our approach is the lack of compactness of the energydue to the critical exponential growth of the nonlinear term <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$ f $</EquationSource> </InlineEquation>.</p>

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On a Logarithmic Weighted Problem on the Whole Euclidean Space \( 𝕉^{4} \) Involving Exponential Growth Nonlinearity

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • S. Baraket,
  • B. Dridi,
  • R. Jaidane,
  • W. Mtaouaa

摘要

In this work, we mainly study a weighted fourth-order problem in $ 𝕉^{4} $ .According to the Adams-type inequalities,we assume the nonlinearity to have a critical or subcritical exponential growth.We establish the existence of a weak solution to this problem by usingthe mountain pass theorem.The major difficulty in our approach is the lack of compactness of the energydue to the critical exponential growth of the nonlinear term $ f $ .