<abstract xmlns="http://www.w3.org/1999/xhtml">We provide sufficient conditions for the existence of periodic solutions for the class of Duffing differential equations<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2019-0007_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>x</mi><mo>″</mo></msup><mo>+</mo><mi>c</mi><mo>(</mo><mi>t</mi><mo>)</mo><msup><mi>x</mi><mo>′</mo></msup><mo>+</mo><mi>a</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>(</mo><mi>t</mi><mo>)</mo><msup><mrow><mi>x</mi></mrow><mn>3</mn></msup><mo>=</mo><mi>h</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo><mo>,</mo></mrow></math><tex-math>x'' + c(t)x' + a(t)x + b(t){x^3} = h(t,x),</tex-math></alternatives></disp-formula>where the functions <italic>a</italic>(<italic>t</italic>), <italic>b</italic>(<italic>t</italic>), <italic>c</italic>(<italic>t</italic>) and <italic>h</italic>(<italic>t</italic>, <italic>x</italic>) are <italic>C</italic>2 and <italic>T</italic>–periodic in the variable <italic>t</italic>.</abstract>

We provide sufficient conditions for the existence of periodic solutions for the class of Duffing differential equationsx″+c(t)x′+a(t)x+b(t)x3=h(t,x),x'' + c(t)x' + a(t)x + b(t){x^3} = h(t,x),where the functions a(t), b(t), c(t) and h(t, x) are C2 and T–periodic in the variable t.

Periodic solutions for a class of Duffing differential equations

Moroccan Journal of Pure and Applied Analysis

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

{"article-title":"Periodic solutions for a class of Duffing differential equations"}

We provide sufficient conditions for the existence of periodic solutions for the class of Duffing differential equationsx″+c(t)x′+a(t)x+b(t)x3=h(t,x),x'' +...

Periodic solutions for a class of Duffing differential equations

Publié en ligne: 08 nov. 2019

Pages: 86 - 103

Reçu: 31 août 2019

Accepté: 06 oct. 2019

DOI: https://doi.org/10.2478/mjpaa-2019-0007

Mots clés
Periodic solution, averaging method, Duffing differential equation

© 2019 Amina Feddaoui et al., published by Sciendo

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

Periodic solutions for a class of Duffing differential equations

Publié en ligne: 08 nov. 2019

Pages: 86 - 103

Reçu: 31 août 2019

Accepté: 06 oct. 2019

DOI: https://doi.org/10.2478/mjpaa-2019-0007

Mots clésPeriodic solution, averaging method, Duffing differential equation

© 2019 Amina Feddaoui et al., published by Sciendo

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

Mots clés
Periodic solution, averaging method, Duffing differential equation