Existence of solutions of nonlinear mixed two-point boundary value problems for third-order nonlinear differential equation (Q1760615)

Summary: The authors use the upper and lower solutions method to study the existence of solutions of nonlinear mixed two-point boundary value problems for third-order nonlinear differential equations. They consider the third-order nonlinear ordinary differential equation \[ y''' = f(x, y, y', y'') \] together with the nonlinear mixed two-point boundary conditions \[ y'(b) = h(y'(a)), \] \[ p(y(a), y(b), y'(a), y'(b)) = 0, \] \[ g(y(a), y(b), y'(a), y'(b), y''(a), y''(b)) = 0. \] Some new existence results are obtained by developing the upper and lower solutions method. Applications are also presented.