Uniqueness and existence for perturbed focal boundary value problems
The author considers the existence and uniqueness of a solution to the equation \[ y^{(n)}=f(t, y, y',\dots, y^{(n-1)})\tag{1} \] satisfying the nonlinear boundary conditions \[ a_{ii}y(t_i)+a_{i,i+1}y'(t_i)+\dots+a_{i,n}y^{(n-1)}(t_i)+B_i(y(t_i), \dots, y^{(n-1)}(t_i))=y_i, \tag{2} \] \(i=1, 2, \dots, n\). Assume that for each solution of equation (1), the solution to the variational boundary value problem is unique. The author proves the existence and uniqueness of the solution to the boundary value problem (1), (2), which generalizes the focal boundary value problems.
scientific article; zbMATH DE number 5001484