A mixed Dirichlet-Robin problem for a nonlinear Kirchhoff-Carrier wave equation

In this paper, a mixed Dirichlet-Robin problem for a nonlinear Kirchhoff-Carrier wave equation is studied. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, we prove the existence and uniqueness of a weak solution of the above problem. An asymptotic expansion of high order in many small parameters of solutions is also discussed.     

Local asymptotic normality for multivariate nonlinear AR processes

In this paper, we establish local asymptotic normality (LAN) for the log-likelihood ratio of a class of multivariate nonlinear autoregressive processes generated by independent identically distributed (i.i.d.) random vectors. This result generalizes LAN for multivariate linear processes to multivariate nonlinear autoregressive processes.     

Discrete Dichotomies and Asymptotic Behavior for Abstract Retarded Functional Difference Equations in Phase Space

We study the problem of asymptotic behavior between weighted bounded solutions of a system of homogeneous linear functional difference equations and its perturbation under non-classical dichotomic properties and also we obtain some results about approximation. We apply our results to Volterra difference systems with infinite delay.     

On the Recursive Sequence

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation?in the title is investigated, where all the coefficients are nonnegative real numbers. The paper is motivated by an open problem proposed by Ladas [Open problems and conjectures, J. Differ. Equations?Appl., 5 (1999), 211–215].