Extremal solutions for third-order nonlinear problems with upper and lower solutions in reversed order

The proof follows from monotone iterative techniques which are based on suitable anti-maximum principles for adequate operators. To deduce such results, we study some related problems coupled with boundary value conditions of the formp0u(a)-q0u′(a)=A,p1u(b)+q1u′(b)=B,u″(a)=C,andu(a)=A,u′(a)=B,u″(b)=C.