NP [SSA]

In this paper, we give a different method from Ao and Zou (2019) and Chen and Zou (2012) to consider the following nonlinear Schrodinger system with one critical exponent and one subcritical exponent: {-Delta(p)u + mu vertical bar u vertical bar(p-2)u = vertical bar u vertical bar(q-2)u + alpha lambda vertical bar u vertical bar(alpha-2)u vertical bar v vertical bar(beta) in R-N, -Delta(p)v + nu vertical bar v vertical bar(p-2)v = vertical bar v vertical bar(p)*(-2)v + beta lambda vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta-2)v in R-N, where N >= max{3, p}, mu, nu, lambda > 0, alpha >= 1, beta >= 1, 2 <= p < q < p* and alpha + beta = p, p* = Np/(N - p). By using variational methods, we prove that there exists mu(0) is an element of (0, 1), such that when 0 < mu <= mu(0), the above system has a positive ground state solution; when mu > mu(0), there exists lambda(mu,nu) is an element of [(mu-mu(0)/alpha)(alpha/p) (nu/beta)(beta/p), (mu/alpha)(alpha/p) (nu/beta)(beta/p)) such that if lambda > lambda(mu,nu), the above system has a positive ground state solution, if lambda < lambda(mu,nu), the above system has no ground state solution. (C) 2020 Elsevier Ltd. All rights reserved.

We report the sensing performance of In2O3 nanoparticles (NPs) synthesized by a co-precipitation method for the detection of isoprene. The as-synthesized In2O3 NPs exhibited excellent isoprene-sensing performance compared to other previously reported isoprene sensors based on metal-oxide semiconductors. Under an exposure of 1 ppm isoprene at an optimal operating temperature of 350 degrees C, the In2O3 NP sensor showed the highest sensing response of similar to 231 with a rapid response time of similar to 3 s. The low detection limit was approximately 0.001 ppm of isoprene. Furthermore, the In2O3 NP sensor showed a good long-term stability for 90 days by controlling the annealing time. In addition, for the sensor's practical applications to a breath isoprene analyzer, we tested the sensing ability of the In2O3 NPs by integrating the sensor into a miniaturized gas analyzer based on gas chromatography (GC). The results revealed that the In2O3 NP sensor is sensitive and can distinctly detect 1 ppm isoprene and 10 ppm H-2 within similar to 100 s in a mixture gas with other breath gases, such as acetone, CO2, CO, and CH4. Our study demonstrated the potential of the In2O3 NP sensor for application in breath isoprene analyzers by controlling the sensor's annealing time and adopting the GC system.