<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we investigate the existence of a positive solution to the third-order boundary value problem
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2021-0006_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mo>{</mo> <mtable columnalign="left"><mtr><mtd><mo>-</mo><msup><mi>u</mi><mo>‴</mo></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><msup><mrow><mi>k</mi></mrow><mn>2</mn></msup><msup><mi>u</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>φ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>f</mi><mrow><mo>(</mo><mrow><mi>t</mi><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msup><mi>u</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow><mo>,</mo><mi> </mi><mi> </mi><mi> </mi><mi>t</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>u</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msup><mi>u</mi><mo>′</mo></msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msup><mi>u</mi><mo>′</mo></msup><mrow><mo>(</mo><mrow><mo>+</mo><mo>∞</mo></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>,</mo></mtd></mtr></mtable></mrow></mrow></math>
<tex-math>\left\{ \matrix{- u'''\left( t \right) + {k^2}u'\left( t \right) = \phi \left( t \right)f\left( {t,u\left( t \right),u'\left( t \right)} \right),\,\,\,t > 0 \hfill \cr u\left( 0 \right) = u'\left( 0 \right) = u'\left( { + \infty } \right) = 0, \hfill \cr} \right.</tex-math>
</alternatives>
</disp-formula> where k is a positive constant, ϕ ∈ L1 (0;+ ∞) is nonnegative and does vanish identically on (0;+ ∞) and the function f : ℝ+ × (0;+ ∞) × (0;+ ∞) → ℝ+ is continuous and may be singular at the space variable and at its derivative.
</abstract>

In this paper, we investigate the existence of a positive solution to the third-order boundary value problem



{ -u‴(t)+k2u′(t)=φ(t)f(t,u(t),u′(t)),   t>0u(0)=u′(0)=u′(+∞)=0,
\left\{ \matrix{- u'''\left( t \right) + {k^2}u'\left( t \right) = \phi \left( t \right)f\left( {t,u\left( t \right),u'\left( t \right)} \right),\,\,\,t > 0 \hfill \cr u\left( 0 \right) = u'\left( 0 \right) = u'\left( { + \infty } \right) = 0, \hfill \cr} \right.

 where k is a positive constant, ϕ ∈ L1 (0;+ ∞) is nonnegative and does vanish identically on (0;+ ∞) and the function f : ℝ+ × (0;+ ∞) × (0;+ ∞) → ℝ+ is continuous and may be singular at the space variable and at its derivative.

Positive solution for singular third-order BVPs on the half line with first-order derivative dependence

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we investigate the existence of a positive solution to the third-order boundary value problem



{...

Positive solution for singular third-order BVPs on the half line with first-order derivative dependence

Pubblicato online: 26 ago 2021

Pagine: 105 - 126

Ricevuto: 29 giu 2020

DOI: https://doi.org/10.2478/ausm-2021-0006

Parole chiave
third-order BVPs, positive solutions, fixed point theory in cones

© 2021 Abdelhamid Benmezaï et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Positive solution for singular third-order BVPs on the half line with first-order derivative dependence

Pubblicato online: 26 ago 2021

Pagine: 105 - 126

Ricevuto: 29 giu 2020

DOI: https://doi.org/10.2478/ausm-2021-0006

Parole chiavethird-order BVPs, positive solutions, fixed point theory in cones

© 2021 Abdelhamid Benmezaï et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Parole chiave
third-order BVPs, positive solutions, fixed point theory in cones