Uniqueness of solutions for third-order two-point boundary value problems (Q2379891)

The authors investigate some types of two point boundary value problems for the third order differential equations \(x''' = f(t,x, x', x'')\) (\(t\in [0,T]\)). Suppose that \(f\): \([0,T]\times(\mathbb R^n)^3 \to\mathbb R^n\) is an \(L^p\)-Carathédory function with \(1\leq p <\infty\). Under some Lipschitz condition they obtain existence and uniqueness for the problems.