In this paper, we focus our attention on a class of integral equations whose prototype is given by where <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1202_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="196" /> </InlineMediaObject> <EquationSource Format="TEX">$L_0u(x) = \int _{\Omega }K(x,y)u(y)\mathrm{{d}}y$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mn>0</mn> </msub> <mi>u</mi> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mi mathvariant="normal">Ω</mi> </msub> <mi>K</mi> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mrow> <mi>u</mi> <mrow> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mrow> <mi mathvariant="normal">d</mi> <mi>y</mi> </mrow> </math></EquationSource> </InlineEquation>, B(u) is an integral operator and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1202_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega \subset \mathbb {R}^N$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1202_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$N\ge 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, is a bounded domain with smooth boundary. We use sub-supersolutions, bifurcation theory and fixed point theorems.

Some remarks on a dispersal integral operator

期刊论文
发表日期：

2025年5月6日

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Francisco J. S. A. Corrêa,
Natan de Assis Lima

摘要

In this paper, we focus our attention on a class of integral equations whose prototype is given by where $L_0u(x) = \int _{\Omega }K(x,y)u(y)\mathrm{{d}}y$ $L_{0} u (x) = \int_{Ω} K (x, y) u (y) d y$ , B(u) is an integral operator and $\Omega \subset \mathbb {R}^N$ $Ω \subset R^{N}$ , $N\ge 1$ $N \geq 1$ , is a bounded domain with smooth boundary. We use sub-supersolutions, bifurcation theory and fixed point theorems.