TY  - JOUR
A1  - Bagderina, Yulia Yu.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Differential invariants of a class of Lagrangian systems with two degrees of freedom
JF  - Journal of mathematical analysis and applications
KW  - Equivalence
KW  - Differential invariant
KW  - Euler-Lagrange equations
Y1  - 2014
U6  - https://doi.org/10.1016/j.jmaa.2013.08.015
SN  - 0022-247X
SN  - 1096-0813
VL  - 410
IS  - 2
SP  - 733
EP  - 749
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Scattering of trajectories at a separatrix under autoresonance
JF  - Journal of mathematical physics
N2  - The subject of this paper is solutions of an autoresonance equation. We look for a connection between the parameters of the solution bounded as t -> -infinity, and the parameters of two two-parameter families of solutions as t -> infinity. One family consists of the solutions which are not captured into resonance, and another of those increasing solutions which are captured into resonance. In this way we describe the transition through the separatrix for equations with slowly varying parameters and get an estimate for parameters before the resonance of those solutions which may be captured into autoresonance. (C) 2014 AIP Publishing LLC.
Y1  - 2014
U6  - https://doi.org/10.1063/1.4875105
SN  - 0022-2488
SN  - 1089-7658
VL  - 55
IS  - 6
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Normally solvable nonlinear boundary value problems
JF  - Nonlinear analysis : theory, methods & applications ; an international multidisciplinary journal
N2  - We investigate nonlinear problems which appear as Euler-Lagrange equations for a variational problem. They include in particular variational boundary value problems for nonlinear elliptic equations studied by F. Browder in the 1960s. We establish a solvability criterion of such problems and elaborate an efficient orthogonal projection method for constructing approximate solutions.
KW  - Nonlinear Laplace operator
KW  - Boundary value problem
KW  - Dirichlet to Neumann operator
Y1  - 2014
U6  - https://doi.org/10.1016/j.na.2013.09.024
SN  - 0362-546X
SN  - 1873-5215
VL  - 95
SP  - 468
EP  - 482
PB  - Elsevier
CY  - Oxford
ER  - 
TY  - JOUR
A1  - Kiselev, Oleg M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The capture of a particle into resonance at potential hole with dissipative perturbation
JF  - Chaos, solitons & fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science
N2  - We study the capture of a particle into resonance at a potential hole with dissipative perturbation and external periodic excitation. The measure of resonance solutions is evaluated. We also derive an asymptotic formula for the parameter range of those solutions which are captured into resonance.
Y1  - 2014
U6  - https://doi.org/10.1016/j.chaos.2013.11.003
SN  - 0960-0779
SN  - 1873-2887
VL  - 58
SP  - 27
EP  - 39
PB  - Elsevier
CY  - Oxford
ER  -