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a b s t r a c tWe establish some oscillation criteria for the two-dimensional dynamic systemon a time scale T. Our results not only unify the oscillation of two-dimensional differential systems and difference systems, but include the oscillation results for differential systems and provide new oscillation criteria for difference systems. Several examples are considered to illustrate the main results.Crown

In this paper, we consider exact controllability to trajectories for a semilinear heat equation with nonlinearity that has superlinear growth at infinity with Dirichlet boundary conditions in a bounded domain of R N . The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem and generalize the previous results.

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