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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 non-cooperative system has the nature of a zero-sum game. A new local characterization for multiple unstable solutions is then established, under(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 self-similar non-vortex solutions of nonlinear Schrödinger equations (NLSE) (cf. [4] and [5]). However, those solutions have infinite L 2 norm so one may not maintain the ring profile all the way up to the singularity. To find self-similar H 1 non-vortex solutions with ring profiles, we study(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 2 norm so one may not maintain the ring profile all the way up to the singularity. To find H 1 non-vortex blowup solutions with ring profiles, we study blowup solutions of(More)
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)
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