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<p>In this paper, we investigate the existence of solutions to a weighted problem involving an operator of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\frac{N}{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> </math></EquationSource> </InlineEquation> biharmonic type within the unit ball <i>B</i> in <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mathbb {R}^{N}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </math></EquationSource> </InlineEquation>. We assume that the non-linearity exhibits critical or subcritical exponential growth with respect to logarithmic Adams-type inequalities. Using the mountain pass Theorem, we establish the existence of a weak solution. The main difficulty lies in the lack of compactness of the energy caused by the critical exponential growth of the non-linear term <i>f</i>. To avoid this problem, we introduce an appropriate asymptotic condition.</p>

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On a logarithmic weighted problem of \(\frac{N}{2}\) biharmonic type on the unit ball of \(\mathbb {R}^{N}\) involving exponential growth non linearity

  • 期刊论文

  • 发表日期：

    2025年11月7日

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  • Rached Jaidane

摘要

In this paper, we investigate the existence of solutions to a weighted problem involving an operator of \(\frac{N}{2}\) N 2 biharmonic type within the unit ball B in \(\mathbb {R}^{N}\) R N . We assume that the non-linearity exhibits critical or subcritical exponential growth with respect to logarithmic Adams-type inequalities. Using the mountain pass Theorem, we establish the existence of a weak solution. The main difficulty lies in the lack of compactness of the energy caused by the critical exponential growth of the non-linear term f. To avoid this problem, we introduce an appropriate asymptotic condition.