Uniqueness and existence for right focal problems via variational equations (Q1310381)

The author is concerned with solutions of right focal boundary value problems for the \(n\)th order differential equation (1) \(y^{(n)}=f(t,y,y', \dots,y^{(n-1)})\), where \(f(t,y_ 1,y_ 2,\dots,y_ n)\) is continuous on \((a,b) \times \mathbb{R}^ n\); \(\partial f/ \partial y_ i\), \(1 \leq i \leq n\), exist and are continuous on \((a,b) \times \mathbb{R}^ n\); solutions of initial value problems for (1) exist on \((a,b)\). Uniqueness and existence are proved via consideration of some variational boundary value problems for the original problems on the base of some uniqueness assumptions on the variational problems.