Gritsans, ArmandsSadyrbaev, FelixYermachenko, Inara2022-01-052022-01-052018-01-24Gritsans, A., Sadyrbaev, F., & Yermachenko, I. (2018). Dirichlet boundary value problem for a system of n second order asymptotically asymmetric differential equations. Electronic Journal of Differential Equations, 2018(35), pp. 1-16.1072-6691https://hdl.handle.net/10877/15091We 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.Text16 pages1 file (.pdf)enAttribution 4.0 InternationalDirichlet boundary value problemRotation of vector fieldAsymptotically asymmetric nonlinearitiesIndex of isolated singular pointFucik spectrumArticle