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Abstract:In this paper, we investigate the existence and uniqueness of solutions of two-point fuzzy boundary value problems for second-order fuzzy differential equations. Some sufficient conditions are presented that guarantee the existence and uniqueness of solutions under the approach of Hukuhara differentiability.

In this article two point fuzzy boundary value problem is defined under the approach generalized Hukuhara differentiability (gH-differentiability). We research the solution method of the fuzzy boundary problem with the basic solutions Φ (x, λ) and χ (x, λ) which are defined by the special procuder. We give operator-theoretical formulation, construct fundamental solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions of the considered fuzzy problem. Then results of the proposed method are illustrated with a numerical example.

In this paper, we present a new discontinuous Sturm-Liouville problem with symmetrically located discontinuities which are defined depending on a parameter in the neighborhood of an interior point in the interval. Also the problem contains an eigenparameter in a boundary condition. We investigate some spectral properties of the eigenvalues, obtain asymptotic formulae for the eigenvalues and the corresponding eigenfunctions and construct Green's function for the problem. We give an illustrative example with tables and figures at the end of the paper.

In this paper, we obtain a regularized trace formula for a Sturm Liouville problem which has two points of discontinuity and also contains an eigenparameter in a boundary ondition.