The authors prove the existence of at least one solution to the fully nonlinear boundary problem
where and , and , , are continuous functions that satisfy some monotonicity properties.
Such solution is given as the limit of a sequence of solutions to adequate truncated problems. The result follows from Schauder’s fixed-point and Kamke’s convergence theorem.
Similar results can be obtained for different choices of . The th-order problem is also studied under analogous arguments.