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- W3175348785 abstract "In this work, the existence of at least one solution for the following third-order integral and <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mi>m</mi> </math> -point boundary value problem on the half-line at resonance <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <msup> <mrow> <mfenced open=( close=)> <mrow> <mi>ρ</mi> <mfenced open=( close=)> <mrow> <mi>t</mi> </mrow> </mfenced> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mfenced open=( close=)> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </mfenced> </mrow> <mrow> <mo>″</mo> </mrow> </msup> <mo>=</mo> <mi>w</mi> <mfenced open=( close=)> <mrow> <mi>t</mi> <mo>,</mo> <mi>u</mi> <mfenced open=( close=)> <mrow> <mi>t</mi> </mrow> </mfenced> <mo>,</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mfenced open=( close=)> <mrow> <mi>t</mi> </mrow> </mfenced> <mo>,</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>″</mo> </mrow> </msup> <mfenced open=( close=)> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </mfenced> <mo>,</mo> <mi>t</mi> <mo>∈</mo> <mfenced open=[ close=)> <mrow> <mn>0</mn> <mo>,</mo> <mrow> <mo>∞</mo> </mrow> </mrow> </mfenced> <mo>,</mo> <mi>u</mi> <mfenced open=( close=)> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <msubsup> <mrow> <mo>∑</mo> </mrow> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>m</mi> </mrow> </msubsup> <mtext> </mtext> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <msubsup> <mrow> <mo>∫</mo> </mrow> <mrow> <mn>0</mn> </mrow> <mrow> <msub> <mrow> <mi>η</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> </msubsup> <mtext> </mtext> <mi>u</mi> <mfenced open=( close=)> <mrow> <mi>t</mi> </mrow> </mfenced> <mi>d</mi> <mi>t</mi> <mo>,</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mfenced open=( close=)> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0</mn> <mo>,</mo> <munder> <mrow> <mi mathvariant=normal>lim</mi> </mrow> <mrow> <mi>t</mi> <mrow> <mo>⟶</mo> </mrow> <mrow> <mo>∞</mo> </mrow> </mrow> </munder> <msup> <mrow> <mfenced open=( close=)> <mrow> <mi>ρ</mi> <mfenced open=( close=)> <mrow> <mi>t</mi> </mrow> </mfenced> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mfenced open=( close=)> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </mfenced> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mo>,</mo> </math> will be investigated. The Mawhin’s coincidence degree theory will be used to obtain existence results while an example will be used to validate the result obatined." @default.
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- W3175348785 date "2021-06-30" @default.
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- W3175348785 title "On the Solvability of a Resonant Third-Order Integral m-Point Boundary Value Problem on the Half-Line" @default.
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- W3175348785 doi "https://doi.org/10.1155/2021/8870108" @default.
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