This work deals with a class of nonlinear viscoelastic wave equations with strong damping and variable exponent sources. The main interest of this paper compared to many previous works in the literature is able to use the idea of potential well method to study both the finite time blow-up for solutions starting from the unstable sets and decay estimate for global solutions starting in the potential wells.

Let d ∈ {3, 4, 5,...} and p ∈ (0, 1]. We consider the Hermite operator L = −Δ + |x|2 on its maximal domain in L2(ℝd). Let HpL(Rd) be the completion of {f∈L2(Rd):MLf∈Lp(Rd)} with respect to the quasi-norm ∥⋅∥HpL=∥ML⋅∥Lp, where MLf(⋅)=supt>0∣∣e−tLf(⋅)∣∣ for all f ∈ L2(ℝd). We characterise HpL(Rd) in terms of Lusin integrals associated with the Hermite operator for p∈(dd+1,1].

The current study examined firm quality and competitiveness using process, market and information strategy and logistics coordination effectiveness in manufacturing industry of Malaysia. The study used survey methodology and the respondents were gathered via convenience sampling. The data analysis was conducted using PLS-SEM. Furthermore, the outcome of study showed that information strategy was found insignificant towards firm quality and competitiveness. However, the information strategy was significantly affecting the logistics coordination effectiveness. Moreover, logistics coordination effectiveness was significantly affecting the firm quality and competitiveness. The market strategy was significantly affecting firm competitiveness. Additionally, market strategy was significantly affecting the logistics coordination effectiveness. Also, process strategy was not significantly affecting the firm competitiveness; however, process strategy was significantly affecting the logistics coordination effectiveness. Moreover, logistics coordination effectiveness was significantly mediating the relationship between all three strategies namely market strategy, process strategy and process strategy and firm competitiveness.

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