A parameter robust method for singularly perturbed delay differential equations.
An exponentially fitted method for singularly perturbed delay differential equations.
Continuous dependence and differentiability of solutions with respect to initial data and right-hand side for differential equations with deviating argument.
Convergence for hyperbolic singular perturbation of integrodifferential equations.
Gamma-convergence results for phase-field approximations of the 2D-Euler Elastica Functional
We establish some new results about the Γ-limit, with respect to the L1-topology, of two different (but related) phase-field approximations ℰ ε ε , x10ff65; ℰ ε ε of the so-called Euler’s Elastica Bending Energy for curves in the plane. In particular we characterize theΓ-limit as ε → 0 of ℰε, and show that in general the Γ-limits of ℰεand x10ff65; ℰ ε do not coincide on indicator functions of sets with non-smooth boundary. More precisely we show that the domain of theΓ-limit of x10ff65;...
Multiple positive solutions to singular boundary value problems for superlinear second order FDEs
We study the existence of positive solutions to the singular boundary value problem for a second-order FDE ⎧ u'' + q(t) f(t,u(w(t))) = 0, for almost all 0 < t < 1, ⎨ u(t) = ξ(t), a ≤ t ≤ 0, ⎩ u(t) = η(t), 1 ≤ t ≤ b, where q(t) may be singular at t = 0 and t = 1, f(t,u) may be superlinear at u = ∞ and singular at u = 0.
Parameter-uniform fitted mesh method for singularly perturbed delay differential equations with layer behavior.
Singularly perturbed set of periodic functional-differential equations arising in optimal control theory
We consider the singularly perturbed set of periodic functional-differential matrix Riccati equations, associated with a periodic linear-quadratic optimal control problem for a singularly perturbed delay system. The delay is small of order of a small positive multiplier for a part of the derivatives in the system. A zero-order asymptotic solution to this set of Riccati equations is constructed and justified.
Structure of stable solutions of a one-dimensional variational problem
We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double...
Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation.
Бифуркационные особенности сингулярно возмущенного уравнения с запаздыванием.