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This paper is concerned with the problem of H8 control of linear neutral systems with time-varying delay. Firstly, by applying a novel Lyapunov-Krasovskii functionalwhich is constructed with the idea of delay partitioning approach, appropriate free-weighting matrices, an improved delay-dependent bounded real lemma (BRL) for neutral systems is established. By using the obtained BRL, a delay-dependent sufficient condition for the existence of a state-feedback controller, which ensures asymptotic stability and a prescribed H8 performance level of the corresponding closed-loop system, is formulated in terms of linear matrix inequalities. Some numerical examples are given to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and multiplicity solutions for the following Klein-Gordon-Maxwell system ∫-Δu + V(x)u - (2ω + ϕ)ϕu = f (x, u), x ∈ R³, Δϕ = (ω + ϕ)u², x ∊ R³, where ω > 0 is a constant and the nonlinearity f (x, u) is either asymptotically linear in u at infinity or the primitive of f (x, u) is of 4-superlinear growth in u at infinity. Under some suitable assumptions, the existence and multiplicity of solutions are proved by using the Mountain Pass theorem and the fountain theorem, respectively. [ABSTRACT FROM AUTHOR]

This article concerns the nonhomogeneous Klein-Gordon equation coupled with a Born-Infeld type equation, ... where ω is a positive constant. We obtain the existence of two solutions using the Mountain Pass Theorem, and the Ekeland's variational principle in critical point theory. [ABSTRACT FROM AUTHOR]

New organic heteropolyacid (HPA) salts prepared by exchanging counter protons of Keggin HPAs with N-methyl-2-pyrrolidonium proved to be highly efficient, conveniently recoverable, and steadily reusable heterogeneous catalysts for the organic solvent-free Prins reactions of styrenes with formalin. [ABSTRACT FROM AUTHOR]