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
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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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