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<p>This study explores the existence of ground state solutions for a Hamiltonian elliptic system in the whole plane <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2060_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">R</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$\mathbb{R}^{2}$</EquationSource> </InlineEquation>, involving double exponential growth nonlinearities, which are given by the Trudinger–Moser inequalities in weighted radial Sobolev spaces. To find solutions, we apply a minimizing process on a generalized Nehari manifold.</p>

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Ground state solutions for Hamiltonian systems with double exponential growth

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  • 出版模式：

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  • 发表日期：

    2025年5月14日

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  • Yony Raúl Santaria Leuyacc

摘要

This study explores the existence of ground state solutions for a Hamiltonian elliptic system in the whole plane R 2 $\mathbb{R}^{2}$ , involving double exponential growth nonlinearities, which are given by the Trudinger–Moser inequalities in weighted radial Sobolev spaces. To find solutions, we apply a minimizing process on a generalized Nehari manifold.