Boundary value problems for functional differential systems
Consider the boundary value problem \[ \begin{gathered} x''(t)+ a_1(t) f(x_t, y_t)= 0,\;y''(t)+ a_2(t) g(x_t, y_t)= 0,\\ x(t)- \beta_1 x'(t)= \xi_1(t)\quad\text{for }-\tau\leq t\leq 0,\\ y(t)- \beta_2 y'(t)= \xi_2(t)\quad\text{for }-\tau\leq t\leq 0,\\ x(1)+ \delta_1 x'(1)= 0,\;y(1)+\delta_2 y'(1)= 0,\end{gathered}\tag{\(*\)} \] where the functions \(a_1\) and \(a_2\) may be singular at \(t= 0,1\). The authors present sufficient conditions for \((*)\) to have at least one, two or three positive solutions. The proofs are based on the fixed point index for completely continuous operators mapping a cone into itself.
scientific article; zbMATH DE number 5074016