| Popis: |
We consider systems of the form $$\displaylines{ x_1''+ g_1(x_1) = h_1(x_1,x_2,\ldots,x_n),\cr x_2''+ g_2(x_2) = h_2(x_1,x_2,\ldots,x_n),\cr \cdots \cr x_n''+ g_n(x_n) = h_n(x_1,x_2,\ldots,x_n) }$$ along with the boundary conditions $$ x_1(0)=x_2(0)=\dots=x_n(0)=0=x_1(1)=x_2(1)=\dots=x_n(1)\,. $$ We assume that right sides are bounded continuous functions, and satisfy $h_i(0,0,\ldots,0)=0$. Also we assume that $g_i(x_i)$ are asymptotically asymmetric functions. By using vector field rotation theory, we provide the existence of solutions. |
