We consider differential operators with separate boundary conditions in this study. And we find a new expression and their derivative of six linearly independent solution. And it will also prove the existence of uniqueness for separate boundary conditions. We obtain asymptotic formulas for the individual values and functions of these problems with boundary value where the potential q (x) is an arbitrary complex function valued in [a, b].

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This paper addresses an eigenvalue problem generated by sixth order differential equations with suitable boundary conditions, which contain a spectral parameter. The asymptotic expressions for sixth order linearly independent solutions as well as new asymptotic formulas for the eigenvalues with eigenfunctions of the boundary value problem are obtained.