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Using numerical experiments to discover theorems in differential equations
1.  Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 016092247, United States 
[1] 
Björn Gebhard. Periodic solutions for the Nvortex problem via a superposition principle. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 54435460. doi: 10.3934/dcds.2018240 
[2] 
ZhongJie Han, Zhuangyi Liu, Jing Wang. Sharper and finer energy decay rate for an elastic string with localized KelvinVoigt damping. Discrete and Continuous Dynamical Systems  S, 2022, 15 (6) : 14551467. doi: 10.3934/dcdss.2022031 
[3] 
Josef DiblÍk, Rigoberto Medina. Exact asymptotics of positive solutions to Dickman equation. Discrete and Continuous Dynamical Systems  B, 2018, 23 (1) : 101121. doi: 10.3934/dcdsb.2018007 
[4] 
Yan Wang, Yanxiang Zhao, Lei Wang, Aimin Song, Yanping Ma. Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer. Journal of Industrial and Management Optimization, 2018, 14 (2) : 653671. doi: 10.3934/jimo.2017067 
[5] 
Shaolin Ji, Xiaole Xue. A stochastic maximum principle for linear quadratic problem with nonconvex control domain. Mathematical Control and Related Fields, 2019, 9 (3) : 495507. doi: 10.3934/mcrf.2019022 
[6] 
Mitsuru Shibayama. Periodic solutions for a prescribedenergy problem of singular Hamiltonian systems. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 27052715. doi: 10.3934/dcds.2017116 
[7] 
Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure and Applied Analysis, 2004, 3 (3) : 395415. doi: 10.3934/cpaa.2004.3.395 
[8] 
Marco Campo, José R. Fernández, Maria Grazia Naso. A dynamic problem involving a coupled suspension bridge system: Numerical analysis and computational experiments. Evolution Equations and Control Theory, 2019, 8 (3) : 489502. doi: 10.3934/eect.2019024 
[9] 
H. O. Fattorini. The maximum principle in infinite dimension. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 557574. doi: 10.3934/dcds.2000.6.557 
[10] 
Yinzheng Sun, Qin Wang, Kyungwoo Song. Subsonic solutions to a shock diffraction problem by a convex cornered wedge for the pressure gradient system. Communications on Pure and Applied Analysis, 2020, 19 (10) : 48994920. doi: 10.3934/cpaa.2020217 
[11] 
Alexei Heintz, Andrey Piatnitski. Osmosis for nonelectrolyte solvents in permeable periodic porous media. Networks and Heterogeneous Media, 2016, 11 (3) : 471499. doi: 10.3934/nhm.2016005 
[12] 
Chengming Cao, Xiaoping Yuan. Quasiperiodic solutions for perturbed generalized nonlinear vibrating string equation with singularities. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 18671901. doi: 10.3934/dcds.2017079 
[13] 
Andrei V. Dmitruk, Nikolai P. Osmolovskii. Proof of the maximum principle for a problem with state constraints by the vchange of time variable. Discrete and Continuous Dynamical Systems  B, 2019, 24 (5) : 21892204. doi: 10.3934/dcdsb.2019090 
[14] 
Hancheng Guo, Jie Xiong. A secondorder stochastic maximum principle for generalized meanfield singular control problem. Mathematical Control and Related Fields, 2018, 8 (2) : 451473. doi: 10.3934/mcrf.2018018 
[15] 
Miaomiao Chen, Rong Yuan. Maximum principle for the optimal harvesting problem of a sizestagestructured population model. Discrete and Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021245 
[16] 
Zhen Wu, Feng Zhang. Maximum principle for discretetime stochastic optimal control problem and stochastic game. Mathematical Control and Related Fields, 2022, 12 (2) : 475493. doi: 10.3934/mcrf.2021031 
[17] 
Carlo Orrieri. A stochastic maximum principle with dissipativity conditions. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 54995519. doi: 10.3934/dcds.2015.35.5499 
[18] 
Shigeaki Koike, Andrzej Świech. Local maximum principle for $L^p$viscosity solutions of fully nonlinear elliptic PDEs with unbounded coefficients. Communications on Pure and Applied Analysis, 2012, 11 (5) : 18971910. doi: 10.3934/cpaa.2012.11.1897 
[19] 
Cheng Hou Tsang, Boris A. Malomed, Kwok Wing Chow. Exact solutions for periodic and solitary matter waves in nonlinear lattices. Discrete and Continuous Dynamical Systems  S, 2011, 4 (5) : 12991325. doi: 10.3934/dcdss.2011.4.1299 
[20] 
Gabriella Bretti, Maya Briani, Emiliano Cristiani. An easytouse algorithm for simulating traffic flow on networks: Numerical experiments. Discrete and Continuous Dynamical Systems  S, 2014, 7 (3) : 379394. doi: 10.3934/dcdss.2014.7.379 
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