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<p>The main objective of this manuscript is to explore and analyze the existence and multiple solutions of a problem that involves an anisotropic <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1218_Article_IEq3.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\((\overrightarrow{p},\overrightarrow{q})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mover accent="true"> <mi>p</mi> <mo stretchy="false">→</mo> </mover> <mo>,</mo> <mover accent="true"> <mi>q</mi> <mo stretchy="false">→</mo> </mover> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Laplacian-type operator. The motivation behind this investigation arises from the utilization of mathematical models in diverse scientific domains, including image enhancement, epidemic disease propagation, and fluid dynamics. By considering general conditions, we are able to prove a primary result that confirms the existence of a solution. Additionally, we incorporate an Ambrosetti–Rabinowitz type condition to achieve a second solution that focuses on the multiplicity of solutions. Through these findings, we contribute to the understanding and advancement of this particular problem.</p>

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Existence and multiplicity results for a system involving an anisotropic \(({\mathop {p}\limits ^{\rightarrow }},{\mathop {q}\limits ^{\rightarrow }})\)-Laplacian type operator

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • A. Razani,
  • L. S. Tavares,
  • J. Vanterler da C. Sousa

摘要

The main objective of this manuscript is to explore and analyze the existence and multiple solutions of a problem that involves an anisotropic \((\overrightarrow{p},\overrightarrow{q})\) ( p → , q → ) -Laplacian-type operator. The motivation behind this investigation arises from the utilization of mathematical models in diverse scientific domains, including image enhancement, epidemic disease propagation, and fluid dynamics. By considering general conditions, we are able to prove a primary result that confirms the existence of a solution. Additionally, we incorporate an Ambrosetti–Rabinowitz type condition to achieve a second solution that focuses on the multiplicity of solutions. Through these findings, we contribute to the understanding and advancement of this particular problem.