ITM Web Conf.
Volume 34, 2020International Conference on Applied Mathematics and Numerical Methods – third edition (ICAMNM 2020)
|Number of page(s)||10|
|Section||Differential Equations, Dynamical Systems, and Geometry|
|Published online||03 December 2020|
The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach
Department of Applied Mathematics University of Craiova Al. I. Cuza St., 13, 200585 Craiova, Romania
* e-mail: email@example.com
This paper is concerned with the problem of existence and uniqueness of solutions for the semilinear fourth-order diﬀerential equation uiv – ku′′ + a(x)u+c(x) f (u) = 0. Existence and uniqueness is proved using variational methods and maximum principles. We also give a dynamical system approach to the equation. We study the bifurcation of the system and show that the behaviour of the stationary points S (α, 0, 0, 0) depend on the relation between the parameter k and β = f ′(α).
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.