Dirichlet boundary value problem for a system of n second order asymptotically asymmetric differential equations
Texas State University, Department of Mathematics
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.
Dirichlet boundary value problem, Rotation of vector field, Asymptotically asymmetric nonlinearities, Index of isolated singular point, Fucik spectrum
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.