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In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on V, K, a, and f, we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential V is allowed to be sign-changing for the asymptotically linear case. [ABSTRACT FROM AUTHOR]

When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here, we develop a mathematical framework and study numerically and analytically the percolation of interacting networks with feedback-dependency links. For the case that all degree distributions of intra- and inter- connectivity links are Poissonian, we find that for a low density of inter-connectivity links, the system undergoes from second order to first order through hybrid phase transition as coupling strength increases. It implies that the average degree k of inter-connectivity links has a little influence on robustness of the system with a weak coupling strength, which corresponds to the second order transition, but for a strong coupling strength corresponds to the first order transition. That is to say, the system becomes robust as k increases. However, as the average degree k of each network increases, the system becomes robust for any coupling strength. In addition, we find that one can take less cost to design robust system as coupling strength decreases by analyzing minimum average degree kmin of maintaining system stability. Moreover, for high density of inter-connectivity links, we find that the hybrid phase transition region disappears, the first order region becomes larger and second order region becomes smaller. For the case of two coupled scale-free networks, the system also undergoes from second order to first order through hybrid transition as the coupling strength increases. We find that for a weak coupling strength, which corresponds to the second order transitions, feedback dependency links have no effect on robustness of system relative to no-feedback condition, but for strong coupling strength which corresponds to first order or hybrid phase transition, the system is more vulnerable under feedback condition comparing with no-feedback condition. Thus, for designing resilient system, designers should try to avoid the feedback dependency links, because the existence of feedback- dependency links makes the system extremely vulnerable and difficult to defend. [ABSTRACT FROM AUTHOR]

The thermal stability of the standard Ni/SiC and a TiW/Ni/SiC Ohmic contacts was investigated and compared after being aged at 400 °C in the 2N2 atmosphere. The Ohmic contact was characterized using a combination of I-V measurements, the optical microscopic imaging, X-ray diffraction (XRD), and Auger electron spectroscopy (AES) techniques. It is shown that the standard Ni/SiC Ohmic contact failed after being aged at 400 °C for 20 h in the N2 atmosphere, while the TiW/Ni/SiC Ohmic contact could stand after 100 h. The TiW/Ni/SiC Ohmic contact was found kept a smooth surface morphology during the rapid thermal annealing and aging process, while the standard Ni/SiC Ohmic metal surface was found rougher. Both the Ohmic contact deteriorations after high temperature aging could be attributed to the formation of graphite which is confirmed by the XRD results. The XRD and AES results reveal that the better thermal stability of the TiW/Ni/SiC could be explained by the formation of CW3 and TiC, which deter the C atom diffusion to form graphite. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the modified Camassa–Holm equation is Painlevé integrable. We also study the orbital stability problem of negative solitary waves for this integrable equation. It is shown that the negative solitary waves are stable for arbitrary wave speed of propagation. [ABSTRACT FROM AUTHOR]

The Dullin–Gottwald–Holm equation can be described as the unidirectional propagation of surface waves in a shallow water regime. In this paper, we study the orbital stability problem of the peaked solitons (peakons) for the periodic Dullin–Gottwald–Holm equation on the line. By constructing a function only depending on three important conservative laws, we prove that the shapes of peakons are stable under small perturbations. We also demonstrate that the solutions of the Cauchy problem for this equation converge to those of the corresponding periodic Camassa–Holm equation as the linear dispersive parameter converges to zero. [ABSTRACT FROM AUTHOR]

This paper studies low-regularity solutions of the periodic Fornberg–Whitham equation with initial value. The existence and the uniqueness of solutions are proved. The results are illustrated by considering the periodic peakons of the periodic Fornberg–Whitham equation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation. We prove the global existence and uniqueness of solution to the viscous Degasperis–Procesi equation for u0∈L2(R). The local well posedness for u0∈L2(R) has been proven based on the energy estimate. The strong and weak limit behaviors of solution to the viscous Degasperis–Procesi equation are obtained. [ABSTRACT FROM AUTHOR]

This paper studies the problem for optimal control of the viscous Degasperis-Procesi equation. The existence and uniqueness of weak solution to the equation are proved in a short interval. The optimal control of the viscous Degasperis-Procesi equation under boundary condition is given and the existence of optimal solution to the equation is proved. [ABSTRACT FROM AUTHOR]