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<p>In this paper, the author considers the nonlinear <i>p</i>-Laplacian Choquard equation on a weighted lattice graph. Under some suitable conditions on the potential function, the author proves that if the nonlinearity satisfies some growth conditions, the equation under study has a strictly positive solution. Compared with previous results, the conditions on the potential are relaxed and <i>p</i> can take any value in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1187_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\((1,+\infty )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mo>+</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Moreover, to our knowledge, there is currently no existence result for the <i>p</i>-Laplacian Choquard equation with the nonlinearity on lattice graphs.</p>

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The positive solution for the nonlinear p-Laplacian Choquard equation on lattice graphs

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Yang Liu

摘要

In this paper, the author considers the nonlinear p-Laplacian Choquard equation on a weighted lattice graph. Under some suitable conditions on the potential function, the author proves that if the nonlinearity satisfies some growth conditions, the equation under study has a strictly positive solution. Compared with previous results, the conditions on the potential are relaxed and p can take any value in \((1,+\infty )\) ( 1 , + ∞ ) . Moreover, to our knowledge, there is currently no existence result for the p-Laplacian Choquard equation with the nonlinearity on lattice graphs.