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We consider the approximation of martensitic microstructure for a class of martensitic transformations. We model such microstructures by multi-well energy minimization problems with general homogeneous boundary data. Under our assumptions on such boundary data, the underlying microstructure can be nonunique. We first show that any energy-minimizing sequence converges strongly to a unique macroscopic deformation that is precisely the homogeneous deformation in the boundary condition. We then prove a series of estimates for the approximation of admissible deformations to the unique macroscopic deformation of the microstructure and for the closeness of the gradients of admissible deformations to the energy wells.

We obtain several comparison theorems for second order linear dynamic equations on a time scale. These results extend comparison theorems for the continuous case and provide some new results in the discrete case, as well as other more general situations.

We propose a new mixed formulation of the Stokes problem where the extra stress tensor is considered. Based on such a formulation, a mixed finite element is constructed and analyzed. This new finite element has properties analogous to the finite volume methods, namely, the local conservation of the momentum and the mass. Optimal error estimates are derived. For the numerical implementation of this finite element, a hybrid form is presented. This work is a first step towards the treatment of viscoelastic fluid flows by mixed finite element methods.

In this paper, we investigate a class of nonlinear impulsive parabolic systems with delay. Several oscillation criteria are established for such systems subject to two different boundary conditions by employing Gauss' divergence theorem and certain impulsive delay differential inequalities.

We consider the multiplicity and stability of subharmonic solutions of discrete dynamic systems with periodic perturbations, whose existence was established in the first part of this series. Under the hypotheses that the perturbation is locally Lipschitz continuous, we determine the precise number of subharmonic solutions, and we also show that these subharmonic solutions are stable (unstable) provide the periodic orbit of the unperturbed system is stable (unstable).

We apply averaging techniques to establish oscillation and nonoscillation criteria for the self-adjoint matrix dynamic equation LX(t):=[P(t)XΔ(t)]Δ+Q(t)Xσ(t)=0 on a measure chain T . These results extend and unify earlier results for the differential and difference equation case.