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Volume 8, Issue 2
The Unique Solvability and Approximation of BVP for a Nonlinear Fourth Order Kirchhoff Type Equation

Dang Quang A & Nguyen Thanh Huong

DOI: 10.4208/eajam.231017.250118a

East Asian J. Appl. Math., 8 (2018), pp. 323-335.

Published online: 2018-05

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  • Abstract

We reduce a nonlinear fourth order equation of Kirchhoff type to an operator equation for a nonlinear term and establish sufficient conditions for the unique solvability of the original problem. Approximate solutions of the problem are derived by a fast converging iterative method. Numerical examples confirm theoretical results and demonstrate the efficiency of the approach used.

  • Keywords

Beam equation, Kirchhoff type equation, nonlinear equation, unique solvability, iterative method.

  • AMS Subject Headings

34B15, 34L30, 65L10, 65L12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-323, author = {Dang Quang A and Nguyen Thanh Huong}, title = {The Unique Solvability and Approximation of BVP for a Nonlinear Fourth Order Kirchhoff Type Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {2}, pages = {323--335}, abstract = {

We reduce a nonlinear fourth order equation of Kirchhoff type to an operator equation for a nonlinear term and establish sufficient conditions for the unique solvability of the original problem. Approximate solutions of the problem are derived by a fast converging iterative method. Numerical examples confirm theoretical results and demonstrate the efficiency of the approach used.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.231017.250118a}, url = {http://global-sci.org/intro/article_detail/eajam/12208.html} }
TY - JOUR T1 - The Unique Solvability and Approximation of BVP for a Nonlinear Fourth Order Kirchhoff Type Equation AU - Dang Quang A & Nguyen Thanh Huong JO - East Asian Journal on Applied Mathematics VL - 2 SP - 323 EP - 335 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/eajam.231017.250118a UR - https://global-sci.org/intro/article_detail/eajam/12208.html KW - Beam equation, Kirchhoff type equation, nonlinear equation, unique solvability, iterative method. AB -

We reduce a nonlinear fourth order equation of Kirchhoff type to an operator equation for a nonlinear term and establish sufficient conditions for the unique solvability of the original problem. Approximate solutions of the problem are derived by a fast converging iterative method. Numerical examples confirm theoretical results and demonstrate the efficiency of the approach used.

Dang Quang A and Nguyen Thanh Huong. (2018). The Unique Solvability and Approximation of BVP for a Nonlinear Fourth Order Kirchhoff Type Equation. East Asian Journal on Applied Mathematics. 8 (2). 323-335. doi:10.4208/eajam.231017.250118a
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