Xianjin Chen

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Motivated by numerical examples in solving semilinear elliptic PDEs for multiple solutions, some properties of Newton homotopy continuation method, such as its continuation on symmetries, the Morse index and certain functional structures, are established. Those results provide useful information on selecting initial points for the method to find desired(More)
A local min-max-orthogonal method together with its mathematical justification is developed in this paper to solve noncooperative elliptic systems for multiple solutions in an order. First it is discovered that a noncooperative system has the nature of a zero-sum game. A new local characterization for multiple unstable solutions is then established, under(More)
WO3 nanowires (WO3NWs) with high length-diameter ratio have been synthesized through a simple synthetic route without any additive and then used to immobilize hemoglobin (Hb) to fabricate a mediator-free biosensor. The morphology and structure of WO3NWs were characterized by scanning electron microscopy, transmission electronic microscopy and X-ray(More)
In this paper, a local min-orthogonal method is developed to solve cooperative nonlinear elliptic systems for multiple co-existing solutions. A characterization of co-existing critical points of a dual functional is established and used as a mathematical justification for the method. The method is then implemented to numerically solve two coupled nonlinear(More)
Blowup ring profiles have been investigated by finding non-vortex blowup solutions of nonlinear Schrödinger equations (NLSE) (cf. [5] and [6]). However, those solutions have infinite L norm so one may not maintain the ring profile all the way up to the singularity. To find H non-vortex blowup solutions with ring profiles, we study blowup solutions of(More)
Three-dimensional flower-like Bi2WO6 microspheres (3D-Bi2WO6 MSs) have been synthesized through a simple hydrothermal method. The morphology and structure of 3D-Bi2WO6 MSs were characterized by scanning electron microscopy (SEM) and X-ray diffraction (XRD). The 3D-Bi2WO6 MSs subsequently were used to immobilize horseradish peroxidase (HRP) and fabricate a(More)
Blowup ring profiles have been investigated by finding self-similar non-vortex solutions of nonlinear Schrödinger equations (NLSE) (cf. [4] and [5]). However, those solutions have infinite L norm so one may not maintain the ring profile all the way up to the singularity. To find selfsimilar H non-vortex solutions with ring profiles, we study self-similar(More)
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