X. Ren and J. Wei, The BCC lattice in a long range interaction system, SIAM Journal on Applied Mathematics, Vol. 83, Iss. 5 (2023) 1854-1871. https://doi.org/10.1137/22M1511722
X. Ren and G. Zhang, Disc–disc structure in a two-species interacting system on a flat torus, Journal of Nonlinear Science, Vol. 32, No. 1 (February, 2022). https://doi.org/10.1007/s00332-021-09760-y
S. Luo, X. Ren, and J. Wei, Nonhexagonal lattices from a two species interacting system, SIAM Journal on Mathematical Analysis, Vol. 52, No. 2 (2020) 1903-1942. https://doi.org/10.1137/19M1245980
X. Ren and D. Shoup, The impact of the domain boundary on an inhibitory system: interior discs and boundary half discs, Discrete and Continuous Dynamical Systems - Series A, Vol. 40, No. 6 (2020) 3957-3979.
C. Wang, X. Ren and Y. Zhao, Bubble assemblies in ternary systems with long range interaction, Communications in Mathematical Sciences, Vol. 17, No. 8 (2019) 2309-2324.
X. Ren and C. Wang, Stationary disk assemblies in a ternary system with long range interaction, Communications in Contemporary Mathematics, Vol. 21, No. 06 (2019) 1850046.
X. Ren and J. Trageser, A study of pattern forming systems with a fully nonlocal interaction kernel of possibly changing sign, Physica D, Vol. 393 (2019) 9-23.
C.-N. Chen, Y.-S. Choi, Y. Hu and X. Ren, Higher dimensional bubble profiles in a sharp interface limit of the FitzHugh-Nagumo system, SIAM Journal on Mathematical Analysis, Vol. 50, No. 5 (2018) 5072-5095. https://doi.org/10.1137/17M1144933
C.-N. Chen, Y.-S. Choi and X. Ren, Bubbles and droplets in a singular limit of the FitzHugh-Nagumo system, Interfaces and Free Boundaries, Vol. 20, Issue 2 (2018) 165-211.
J. Lu, F. Baginski and X. Ren, Equilibrium configurations of boundary droplets in a self-organizing inhibitory system, SIAM Journal on Applied Dynamical Systems, Vol 17, Issue 2 (2018) 1353-1376. https://doi.org/10.1137/17M113856X
X. Ren and J. Wei, The spectrum of the torus profile to a geometric variational problem with long range interaction,Physica D, Vol. 351-352 (2017) 62-88.
X. Ren and C. Wang, A stationary core-shell assembly in a ternary inhibitory system, Discrete and Continuous Dynamical Systems - Series A, Vol. 37, No. 2 (2017) 983-1012.
X. Ren and D. Shoup, The impact of the domain boundary on an inhibitory system: existence and location of a stationary half disc, Communications in Mathematical Physics, Vol. 340, No. 1 (2015) 355-412.
X. Ren and J. Wei, A double bubble assembly as a new phase of a ternary inhibitory system, Archive for Rational Mechanics and Analysis, Vol. 215, No. 3 (2015) 967-1034.
X. Ren and J. Wei, Asymmetric and symmetric double bubbles in a ternary inhibitory system, SIAM Journal on Mathematical Analysis, Vol. 46, No. 4 (2014) 2798-2852. https://doi.org/10.1137/140955720
X. Ren and J. Wei, Double tori solution to an equation of mean curvature and Newtonian potential, Calculus of Variations and Partial Differential Equations, Vol. 49, No. 3 (2014) 987-1018.
X. Ren and J. Wei, A double bubble in a ternary system with inhibitory long range interaction, Archive for Rational Mechanics and Analysis, Vol. 208, No. 1 (2013) 201-253.
S. Gillmor, J. Lee and X. Ren, The role of Gauss curvature in a membrane phase separation problem, Physica D, Vol 240, No. 24 (2011) 1913-1927.
T. Kolokolnikov and X. Ren, Smoke-ring solutions of Gierer-Meinhardt system in $R^3$, SIAM Journal on Applied Dynamical Systems, Vol. 10, No. 1 (2011), 251-277. https://doi.org/10.1137/100802293
X. Ren and J. Wei, A toroidal tube solution to a problem involving mean curvature and Newtonian potential, Interfaces and Free Boundaries, Vol. 13, No. 1 (2011), 127-154.
X. Kang and X. Ren, The pattern of multiple rings from morphogenesis in development, Journal of Nonlinear Science, Vol. 20, No. 6 (2010), 747-779.
X. Ren and J. Wei, Oval shaped droplet solutions in the saturation process of some pattern formation problems, SIAM Journal on Applied Mathematics, Vol. 70, No. 4 (2009), 1120-1138. https://doi.org/10.1137/080742361
X. Ren and J. Wei, On a phase field problem driven by interface area and interface curvature, European Journal of Applied Mathematics, Vol. 20, No. 6 (2009), 531-556.
X. Ren, Shell structure as solution to a free boundary problem from block copolymer morphology, Discrete and Continuous Dynamical Systems - Series A, Vol. 24, No. 3 (2009), 979-1003.
X. Kang and X. Ren, Ring pattern solutions of a free boundary problem in diblock copolymer morphology, Physica D, Vol. 238, No. 6 (2009), 645-665.
X. Ren and J. Wei, The critical mass constraint in the Cahn-Hilliard equation, Interfaces and Free Boundaries, Vol. 10, No. 3 (2008), 301-338.
M. Helmers, B. Niethammer and X. Ren, Evolution in off-critical diblock copolymer melts, Networks and Heterogeneous Media, Vol. 3, No. 3 (2008), 615-632.
X. Ren and J. Wei, Spherical solutions to a nonlocal free boundary problem from diblock copolymer morphology, SIAM Journal on Mathematical Analysis, Vol. 39, No. 5 (2008), 1497-1535. https://doi.org/10.1137/070690286
X. Ren and J. Wei, Many droplet pattern in the cylindrical phase of diblock copolymer morphology, Reviews in Mathematical Physics, Vol. 19, No. 8 (2007), 879-921.
X. Ren and J. Wei, Single droplet pattern in the cylindrical phase of diblock copolymer morphology, Journal of Nonlinear Science, Vol. 17, No. 5 (2007), 471-503.
E. N. Dancer, X. Ren and S. Yan, On multiple radial solutions of a singularly perturbed nonlinear elliptic system, SIAM Journal on Mathematical Analysis, Vol. 38, No. 6 (2007), 2005-2041. https://doi.org/10.1137/050643507
X. Ren and J. Wei, Existence and stability of spherically layered solutions of the diblock copolymer equation, SIAM Journal on Applied Mathematics, Vol. 66, No. 3 (2006), 1080-1099. https://doi.org/10.1137/040618771
X. Ren and J. Wei, Droplet solutions in the diblock copolymer problem with skewed monomer composition, Calculus of Variations and Partial Differential Equations, Vol. 25, No. 3 (2006), 333-359.
X. Ren and J. Wei, Wriggled lamellar solutions and their stability in the diblock copolymer problem, SIAM Journal on Mathematical Analysis, Vol. 37, No. 2 (2005), 445-489. https://doi.org/10.1137/S0036141003433589
X. Ren and J. Wei, Nucleation in the FitzHugh-Nagumo system: interface-spike solutions, Journal of Differential Equations, Vol. 209, No. 2 (2005), 266-301.
R. Choksi and X. Ren, Diblock copolymer/homopolymer blends: derivation of a density functional theory, Physica D, Vol. 203, No. 1-2 (2005), 100-119.
X. Ren and J. Wei, Chiral symmetry breaking and the soliton-stripe pattern in Langmuir monolayers and smectic films, Nonlinearity, Vol. 17, No. 2 (2004), 617-632.
X. Ren and J. Wei, The soliton-stripe pattern in the Seul-Andelman membrane, Physica D, Vol. 188, No. 3-4 (2004), 277-291.
A. Chmaj and X. Ren, Soliton-stripe patterns of a functional with an attractive-repulsive-attractive interaction, Journal of Dynamics and Differential Equations, Vol. 16, No. 2 (2004), 455-468.
X. Ren and J. Wei, Stability of spot and ring solutions of the diblock copolymer equation, Journal of Mathematical Physics, Vol. 45, No. 11 (2004), 4106-4133.
X. Ren and J. Wei, Triblock copolymer theory: Free energy, disordered phase and weak segregation, Physica D, Vol. 178, No. 1-2 (2003), 103-117.
X. Ren and J. Wei, Triblock copolymer theory: Ordered ABC lamellar phase, Journal of Nonlinear Science, Vol. 13, No. 2 (2003), 175-208.
X. Ren and J. Wei, On the spectra of 3-D lamellar solutions of the diblock copolymer problem, SIAM Journal on Mathematical Analysis, Vol. 35, No. 1 (2003), 1-32. https://doi.org/10.1137/S0036141002413348
X. Ren and J. Wei, On energy minimizers of the di-block copolymer problem, Interfaces and Free Boundaries, Vol. 5, No. 2 (2003), 193-238.
R. Choksi and X. Ren, On the derivation of a density functional theory for microphase separation of diblock copolymers, Journal of Statistical Physics, Vol. 113, No. 1-2 (2003), 151-176.
X. Ren and J. Wei, Soliton-stripe patterns in charged Langmuir monolayers, Journal of Nonlinear Science, Vol. 13, No. 6 (2003), 603-624.
X. Ren and J. Wei, Concentrically layered energy equilibria of the di-block copolymer problem, European Journal of Applied Mathematics, Vol. 13, No. 5 (2002), 479-496.
A. Chmaj and X. Ren, The nonlocal bistable equation: stationary solutions on a bounded interval, Electronic Journal of Differential Equations, Vol. 2002, No. 03 (2002), 1-21.
A. Chmaj and X. Ren, Pattern formation in the nonlocal bistable equation, Methods and Applications of Analysis, Vol. 8, No. 3 (2001), 369-386.
X. Ren and J. Wei, On the multiplicity of solutions of two nonlocal variational problems, SIAM Journal on Mathematical Analysis, Vol. 31, No. 4 (2000), 909-924. https://doi.org/10.1137/S0036141098348176
X. Ren and L. Truskinovsky, Finite scale microstructures in nonlocal elasticity, Journal of Elasticity, Vol. 59, No. 1-3 (2000), 319-355.
A. Chmaj and X. Ren, Multiple layered solutions of the nonlocal bistable equation, Physica D, Vol. 147, No. 1-2 (2000), 135-154.
A. Chmaj and X. Ren, Homoclinic solutions of an integral equation: Existence and stability, Journal of Differential Equations, Vol. 155, No. 1 (1999), 17-43.
P.W. Bates and X. Ren, Heteroclinic orbits for a higher order phase transition problem, European Journal of Applied Mathematics, Vol. 8, No. 2 (1997), 149-163.
P. W. Bates, P. C. Fife, X. Ren and X. Wang, Traveling waves in a convolution model for phase transitions, Archive for Rational Mechanics and Analysis, Vol. 138, No. 2 (1997), 105-136.
X. Ren, A variational approach to multiple layers of the bistable equation in long tubes, Archive for Rational Mechanics and Analysis, Vol. 138, No. 2 (1997), 169-203.
X. Ren and M. Winter, Young measures in a nonlocal phase transition problem, Proceedings of the Royal Society of Edinburgh, 127A, No. 3 (1997), 615-637.
X. Ren, Multi-layer local minimum solutions of the bistable equation in noncylindrical domains, Journal of Differential Equations, Vol. 141, No. 1 (1997), 13-24.
P. W. Bates and X. Ren, Transition layer solutions of a higher order model in an infinite tube, Communications in Partial Differential Equations, Vol. 21, No. 1-2 (1996), 195-220.
X. Ren and J. Wei, Single-point concentration and least-energy solutions, Proceedings of the American Mathematical Society, Vol. 124, No. 1 (1996), 111-120.
X. Ren and J. Wei, Counting peaks of solutions to some quasilinear elliptic equations with large exponents, Journal of Differential Equations, Vol. 117, No. 1 (1995), 28-55.
X. Ren and J. Wei, Asymptotic behavior of energy solutions to a two dimensional semilinear problem with mixed boundary condition, Nonlinear Analysis: Theory, Methods, and Applications, Vol.24, No. 4 (1995), 587-604.
X. Ren and J. Wei, On a semilinear elliptic equation in $R^{2}$ whenthe exponent approaches infinity, Journal of Mathematical Analysis and Applications, Vol. 189, No. 1 (1995), 179-193.
X. Ren and J. Wei, On a two dimensional elliptic problem with large exponent in nonlinearity, Transactions of the American Mathematical Society, Vol. 343, No. 2 (1994), 749-763.
X. Ren, Least-energy solutions to a non-autonomous semilinear problem with small diffusion coefficient, Electronic Journal of Differential Equations, Vol. 1993, No. 05 (1993), 1-21.