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Abstract: In this paper, we consider dynamical behavior of non-autonomous plate-type evolutionary equations with critical nonlinearity. We prove the existence of a uniform attractor in the space . [Copyright &y& Elsevier]

Abstract: This paper deals with the existence and nonexistence of global positive solutions for two evolution P-Laplacian equations in exterior domains with inhomogeneous boundary conditions. We demonstrate that is its critical exponent provided . Furthermore, we prove that if , then every positive solution of the equations blows up in finite time; whereas for , the equations admit the global positive solutions for some boundary value and some initial data . We also demonstrate that every positive solution of the equations blows up in finite time provided . [Copyright &y& Elsevier]

Let w be an infinite fixed point of a binary k-uniform morphism f, and let E(w) be the critical exponent of w. We give necessary and sufficient conditions for E(w) to be bounded, and an explicit formula to compute it when it is. In particular, we show that E(w) is always rational. We also sketch an extension of our method to non-uniform morphisms over general alphabets. [ABSTRACT FROM AUTHOR]