Abstract In this paper, we discuss the existence and approximation of solutions for a fourth-order nonlinear boundary value problem by using quasilinearization technique. presence lower solution α an upper β in reverse order $\alpha \geq \beta $ α ≥ β , show (extreme) solution.

In this paper, the collocation method is considered to solve nonhomogeneous for fourth order fuzzy boundary value problems, which fuzziness appeared together in conditions and term of differential equation. The solution depends on transforming problem equivalent crisp problems using concept α-level sets.