Jann-Long Chern

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In this paper we will apply the method of rotating planes (MRP) to investigate the radial and axial symmetry of the least-energy solutions for semilinear elliptic equations on the Dirichlet and Neumann problems respectively. MRP is a variant of the famous method of moving planes (MMP). One of our main results is to consider the least-energy solutions of the(More)
Reaction–diffusion systems are used to model many chemical and biological phenomena in the natural world [25, 26], and systems of coupled partial differential equations are also used in other physical models such as nonlinear Schrödinger systems in multi-component Bose–Einstein condensates and nonlinear optics [19, 23]. The steady-state solutions or(More)
In this paper, we consider a nonlinear elliptic system which is an extension of the single equation derived by investigating the stationary states of the nonlinear Schrödinger equation. We establish the existence and uniqueness of solutions to the Dirichlet problem on the ball. In addition, the nonexistence of the ground state solutions under certain(More)
In this work we consider smooth orthonormal factorizations of smooth matrixvalued functions of constant rank. In particular, we look at Schur, singular value, and related decompositions. Furthermore, we consider the case in which the functions are periodic and study periodicity of the factors. We allow for eigenvalues and singular values to coalesce.
∗Partially supported by National Science Council of Taiwan. †Partially supported by National Natural Science Foundation of China (10671049), Longjiang Professorship, National Science Foundation of US, and Summer Research Grant of College of William and Mary; part of this work was done when J. Shi visited National Central University in May 2009, and he would(More)
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