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We consider problems of the calculus of variations on unbounded time scales. We prove the validity of the Euler-Lagrange equation on time scales for infinite horizon problems, and a new transversality condition.
In this paper, we study problems of minimization of a functional depending on the fractional Caputo derivative of order $0<\alpha \leq 1$ and the fractional Riemann- Liouville integral of order $\beta > 0$ at fixed endpoints. A fractional…
We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary…
We prove higher-order Euler-Lagrange and DuBois-Reymond stationary conditions to fractional action-like variational problems. More general fractional action-like optimal control problems are also considered.
We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin…
We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.
In this note we give a closed formula for Faltings' delta-invariant of a hyperelliptic Riemann surface.
In this paper we present explicit estimate for Lipschitz constant of solution to a problem of calculus of variations. The approach we use is due to Gamkrelidze and is based on the equivalence of the problem of calculus of variations and a…
We provide a necessary and sufficient condition for matrices in the max-plus algebra to be pseudo-diagonalizable, calculate the powers of pseudo-diagonal matrices and prove the invariance of optimal-node matrices and separable matrices…
We consider an inverse spectral problem that consists in the recovery of the differential expression coefficients for higher-order operators with separated boundary conditions from the spectral data (eigenvalues and weight numbers). This…
We present a method for proving the existence of solutions to a class of one dimensional variational problems. The method is demonstrated by two examples of optimal interpolation problems which are motivated by engineering applications. In…
A unifying framework for some extremal problems on locally compact Abelian groups is considered, special cases of which include the Delsarte and Tur\'an extremal problems. A slight variation of the extremal problem is introduced and the…
The orientation-preservation condition, i.e., the Jacobian determinant of the deformation gradient $\det \nabla u$ is required to be positive, is a natural physical constraint in elasticity as well as in many other fields. It is well known…
In this paper, we trace the development of the theory of the calculus of variations. From its roots in the work of Greek thinkers and continuing through to the Renaissance, we see that advances in physics serve as a catalyst for…
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…
We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.
This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form…
We generalise and sharpen several recent results in the literature regarding the existence and complete classification of the isolated singularities for a broad class of nonlinear elliptic equations of the form \begin{equation} -{\rm…
A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The…
Fractional operators play an important role in modeling nonlocal phenomena and problems involving coarse-grained and fractal spaces. The fractional calculus of variations with functionals depending on derivatives and/or integrals of…