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The following theorem is the indefinite version of the Chaotic Furuta inequality, a result previously stated in the context of Hilbert spaces by Fujii, Furuta and Kamei [5]..

Projecting the equations resulting from the Euler-Lagrange equations and the equations deduced from the application of Noether’s theorem back on the original space provides all

Although Theorem 1.3 gives solutions to the same equation as Theorem 1.1 (if m is the same), the spirit is quite different: While m could take any value in Theorem 1.1 , we have here

On substituting this value g into formula (3.3), we obtain a solution of the second boundary value problem provided that the requirement for the principal vector and the

In this section, starting from the Appel polynomials, we construct a quadra- ture rule generalizing the well known Euler–MacLaurin quadrature formula, using Appel (instead

In the paper [2] the superstability theorem of the d’Alembert functional equation (2) appears.. The

Adjoint equation, fixed points, principal matrix solution, resolvent, variation of parameters, Volterra integro-differential equation.... With this they were able to derive

The concept of a Lepage form allows us to introduce the Euler-Lagrange dis- tribution for variational functionals, depending on velocities, in a similar way as in the calculus