*Correspondence: [email protected] Department of Mathematics, Inner Mongolia University, Hohhot, 010021, China Abstract The present paper deals with the dependence of eigenvalues of 2nth order boundary value transmission problems on the problem. The eigenvalues depend not only continuously but also smoothly on the problem. Some new differential expressions of eigenvalues with respect to an endpoi...

We state a combinatorial conjecture, which, if true, yields a simple solution to the multiplier version of the inverse problem of the calculus of variations. With the help of a computer, we verified our conjecture for 3 ≤ n ≤ 100, and thus found necessary and sufficient conditions for a 2nth-order scalar ordinary differential equation ∂2nu/∂x2n = f (x, u, ∂u/∂x, . . . , ∂2n−1u/∂x2n−1), 3 ≤ n ≤ ...