On the singularities of harmonic maps from a domain in into
On the spectrum of a nonlinear operator
On the structure of the set of curves bounding minimal surfaces of prescribed degeneracy.
On the symmetry of blowup solutions to a mean field equation
On the theory of Sobolev-type classes of functions with values in a metric space.
On the topological charge conservation in the three-dimensional -model.
A field of three-component unit vectors on the dimensional spacetime is considered. Two field configurations with different values of the topological charge cannot be connected by the path of field configurations with a finite Euclidean action. Therefore there is no transition between them. The initial and final configurations are assumed to be continuous at infinity. The asymptotic behaviour of intermediate configurations may be arbitrary. The proof is based on the properties of the degree of...
On the transversal distribution and the complete figure in the second order multiple integral problem in the calculus of variations.
On three-periodic trajectories of multi-dimensional dual billiards.
On two problems studied by A. Ambrosetti
We study the Ambrosetti–Prodi and Ambrosetti–Rabinowitz problems.We prove for the first one the existence of a continuum of solutions with shape of a reflected (-shape). Next, we show that there is a relationship between these two problems.
On Univalent Harmonic Maps Between Surfaces.
On variational impulsive boundary value problems
Using the variational approach, we investigate the existence of solutions and their dependence on functional parameters for classical solutions to the second order impulsive boundary value Dirichlet problems with L1 right hand side.
On weakly harmonic maps and Noether harmonic maps from a Riemann surface into a Riemannian manifold
On -convergence for problems of jumping type.
Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria
In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...
Optimal approximations on Riemannian manifolds.
Optimal control of variational inequality with applications to axisymmetric shells
The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.
Optimal control problems on parallelizable riemannian manifolds : theory and applications
The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group which is also a parallelizable riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions employing calculus...
Optimal control problems on parallelizable Riemannian manifolds: theory and applications
The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group SE(3), which is also a parallelizable Riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions...
Optimal Regularity Theorems for Variational Problems with Obstacles.
Optimization problems on complete Riemannian manifolds