Existence and location results for fully nonlinear boundary value problem of \(n\)th-order nonlinear system
The following boundary value problem \[ \begin{aligned} &y^{(n)} = f(t,y,y',\dots,y^{(n-1)}), \\ &P_i(y(a),y'(a),\dots,y^{(n-1)}(a)) = 0, \quad i=1,2,\dots,n-1, \\ &P_n(y(b),y'(b),\dots,y^{(n-1)}(b)) = 0 \end{aligned} \] is considered, where \(y=(y_1,y_2,\dots,y_m) \in {\mathbb R}^m\), \(f \in C(I \times {\mathbb R}^{mn},{\mathbb R}^m)\), and \(P_i \in C({\mathbb R}^{mn},{\mathbb R}^m)\), \(i=1,2,\dots,n\). Existence results of solutions are obtained. More general problems are also considered.
scientific article; zbMATH DE number 5575253
scientific article