Dirichlet boundary value problem for a system of n second order asymptotically asymmetric differential equations
Date
2018-01-24
Authors
Gritsans, Armands
Sadyrbaev, Felix
Yermachenko, Inara
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider systems of the form
x1″ + g1(x1) = h1(x1, x2,..., xn),
x2″ + g2(x2) = h2(x1, x2,..., xn),
...
xn″ + gn(xn) = hn(x1, x2,..., xn)
along with the boundary conditions
x1(0) = x2(0) = ∙∙∙ = xn(0) = 0 = x1(1) = x2(1) = ∙∙∙ = xn(1).
We assume that right sides are bounded continuous functions, and satisfy hi(0, 0,..., 0) = 0. Also we assume that gi(xi are asymptotically asymmetric functions. By using vector field rotation theory, we provide the existence of solutions.
Description
Keywords
Dirichlet boundary value problem, Rotation of vector field, Asymptotically asymmetric nonlinearities, Index of isolated singular point, Fucik spectrum
Citation
Gritsans, A., Sadyrbaev, F., & Yermachenko, I. (2018). Dirichlet boundary value problem for a system of n second order asymptotically asymmetric differential equations. <i>Electronic Journal of Differential Equations, 2018</i>(35), pp. 1-16.