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<p>This paper investigates the existence and multiplicity of positive solutions to the following semilinear problem: where <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2025_379_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="120" /> </InlineMediaObject> <EquationSource Format="TEX">\(f\in C([0,\infty ),{\mathbb {R}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>∈</mo> <mi>C</mi> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> represents an oscillating nonlinearity that satisfies a type of area condition. Our main analytical tools include variational methods and the sub-supersolution method.</p>

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On positive solutions of fractional elliptic equations with oscillating nonlinearity

  • 期刊论文

  • 发表日期：

    2025年2月21日

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  • Francisco J. S. A. Corrêa,
  • César E. T. Ledesma,
  • Alânnio B. Nóbrega

摘要

This paper investigates the existence and multiplicity of positive solutions to the following semilinear problem: where \(f\in C([0,\infty ),{\mathbb {R}})\) f ∈ C ( [ 0 , ∞ ) , R ) represents an oscillating nonlinearity that satisfies a type of area condition. Our main analytical tools include variational methods and the sub-supersolution method.