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• W3212642271 abstract "The boundary value problem of a fourth-order beam equation <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mfenced open=( close=)> <mrow> <mn>4</mn> </mrow> </mfenced> </mrow> </msup> <mo>=</mo> <mi>λ</mi> <mi>f</mi> <mfenced open=( close=)> <mrow> <mi>x</mi> <mo>,</mo> <mi>u</mi> <mo>,</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>″</mo> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>′</mo> <mo>′</mo> <mo>′</mo> </mrow> </msup> </mrow> </mfenced> <mo>,</mo> <mn>0</mn> <mo>≤</mo> <mi>x</mi> <mo>≤</mo> <mn>1</mn> </math> is investigated. We formulate a nonclassical cantilever beam problem with perturbed ends. By determining appropriate values of <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <mi>λ</mi> </math> and estimates for perturbation measurements on the boundary data, we establish an existence theorem for the problem under integral boundary conditions <math xmlns=http://www.w3.org/1998/Math/MathML id=M3> <mi>u</mi> <mfenced open=( close=)> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mfenced open=( close=)> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <msubsup> <mrow> <mo>∫</mo> </mrow> <mrow> <mn>0</mn> </mrow> <mrow> <mn>1</mn> </mrow> </msubsup> <mi>p</mi> <mfenced open=( close=)> <mrow> <mi>x</mi> </mrow> </mfenced> <mi>u</mi> <mfenced open=( close=)> <mrow> <mi>x</mi> </mrow> </mfenced> <mi>d</mi> <mi>x</mi> <mo>,</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>″</mo> </mrow> </msup> <mfenced open=( close=)> <mrow> <mn>1</mn> </mrow> </mfenced> <mo>=</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>′</mo> <mo>′</mo> <mo>′</mo> </mrow> </msup> <mfenced open=( close=)> <mrow> <mn>1</mn> </mrow> </mfenced> <mo>=</mo> <msubsup> <mrow> <mo>∫</mo> </mrow> <mrow> <mn>0</mn> </mrow> <mrow> <mn>1</mn> </mrow> </msubsup> <mi>q</mi> <mfenced open=( close=)> <mrow> <mi>x</mi> </mrow> </mfenced> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mo>″</mo> </mrow> </msup> <mfenced open=( close=)> <mrow> <mi>x</mi> </mrow> </mfenced> <mi>d</mi> <mi>x</mi> <mo>,</mo> </math> where <math xmlns=http://www.w3.org/1998/Math/MathML id=M4> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>∈</mo> <msup> <mrow> <mi>L</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msup> <mfenced open=[ close=]> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> </mfenced> <mo>,</mo> </math> and <math xmlns=http://www.w3.org/1998/Math/MathML id=M5> <mi>f</mi> </math> is continuous on <math xmlns=http://www.w3.org/1998/Math/MathML id=M6> <mfenced open=[ close=]> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> </mfenced> <mo>×</mo> <mfenced open=[ close=)> <mrow> <mn>0</mn> <mo>,</mo> <mrow> <mo>∞</mo> </mrow> </mrow> </mfenced> <mo>×</mo> <mfenced open=[ close=)> <mrow> <mn>0</mn> <mo>,</mo> <mrow> <mo>∞</mo> </mrow> </mrow> </mfenced> <mo>×</mo> <mfenced close=] open=(> <mrow> <mo>−</mo> <mrow> <mo>∞</mo> </mrow> <mo>,</mo> <mn>0</mn> </mrow> </mfenced> <mo>×</mo> <mfenced close=] open=(> <mrow> <mo>−</mo> <mrow> <mo>∞</mo> </mrow> <mo>,</mo> <mn>0</mn> </mrow> </mfenced> <mo>.</mo> </math>" @default.
• W3212642271 created "2021-11-22" @default.
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• W3212642271 date "2021-11-08" @default.
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• W3212642271 title "A Cantilever Beam Problem with Small Deflections and Perturbed Boundary Data" @default.
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