# Preprints available online

## Submitted Papers and Preprints:

### (with Azahara Delatorre, W. Ao and Mar Gonzalez) A gluing approach for the fractional Yamabe problem with isolated singularities (W. Ao, Hardy Chan and Mar Gonzalez) Existence of positive weak solutions for fractional Lane-Emden equations with prescribed singular sets (with W. Ao and M. Musso) Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrodinger equations (with W. Ao and H. Chan) Boundary concentrations on segments (with WW Ao and J. Yang) Vortex helices for inhomogeneous Gross-Pitaevskii equation in three dimensional spaces (with Hardy Chan) Travelling wave solutions for bistable fractional Allen-Cahn equations with a pyramidal front. (with Changfeng Gui and Yong Liu) Two-end solutions to the Allen-Cahn equation in \$\mathbb{R}^3\$ (with ZM Guo and Feng Zhou) Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation (with ZM Guo) Entire solutions and global bifurcations for a biharmonic equation with singular nonlinearity (with YX Guo) Infinitely many positive solutions for nonlinear Schr\"{o}dinger system with nonsymmetric first order (with S. Kim and M. Musso) A non-compactness result on the fractional Yamabe problem in large dimensions and supplement material (with S. Kim and M. Musso) Existence theorems of the fractional Yamabe problem (with T. Kolokolnikov) Pattern formation in a reaction-diffusion system with space-dependent feed rate (with S Luo and W. Zou) On the triharmonic Lane-Emden equation (with S Luo and W. Zou) Classification of stable solutions to the fractional (\$2 (with S Luo and W. Zou) On finite Morse index solutions to the quaharmonic Lane-Emden equations (with Yong Liu and Kelei Wang) Global minimizers of Allen-Cahn equation in dimensions \$ n\geq 8\$ (with CS Lin and Z. Nie) Classification of solutions to general Toda systems with singular sources (with CS Lin and Z. Nie) Toda system and hypergeometric equations (with CS Lin, W. Yang and L. Zhang) On rank two Toda system with arbitrary singularities: local maxx and new estimates (with Y. Liu) On Helmholtz equation and Dancer's type entire solutions for nonlinear elliptic equations (with CS Lin and W. Yang) Degree counting and shadow system for \$SU(3)\$ Toda system: one bubbling (with X. Ren) The spectrum of the torus profile to a geometric variational problem with long range interaction (with M. Winter) Stability of new spike solutions in a supply chain model (with W. Yan and B. Xu) On Lin-Ni's conjecture in dimension four and six (with Wen Yang) Multi-bump ground states of the fractional Gierer-Meinhardt system on the real line (with Liqun Zhang) On the effect of domain shape on the existence of large solutions of some spuerlinear elliptic problems,

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