| Issue |
ITM Web Conf.
Volume 34, 2020
International Conference on Applied Mathematics and Numerical Methods – third edition (ICAMNM 2020)
|
|
|---|---|---|
| Article Number | 03005 | |
| Number of page(s) | 10 | |
| Section | Differential Equations, Dynamical Systems, and Geometry | |
| DOI | https://doi.org/10.1051/itmconf/20203403005 | |
| 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: cristiandanet@yahoo.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
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