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On the renormalization of Hamiltonian flows, and critical invariant tori
Lipschitz continuous solutions of some doubly nonlinear parabolic equations
1.  Department of Applied Physics, School of Science and Engineering, Waseda University, 341, Okubo, Tokyo, 1698555, Japan 
2.  Department of Mathematics and Computer Science, Tsuda College, 211, Tsudachou, Kodairashi, Tokyo, 1878577, Japan 
[1] 
Predrag S. Stanimirović, Branislav Ivanov, Haifeng Ma, Dijana Mosić. A survey of gradient methods for solving nonlinear optimization. Electronic Research Archive, 2020, 28 (4) : 15731624. doi: 10.3934/era.2020115 
[2] 
Hua Chen, Yawei Wei. Multiple solutions for nonlinear cone degenerate elliptic equations. Communications on Pure & Applied Analysis, , () : . doi: 10.3934/cpaa.2020272 
[3] 
Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, , () : . doi: 10.3934/cpaa.2020276 
[4] 
Huiying Fan, Tao Ma. Parabolic equations involving Laguerre operators and weighted mixednorm estimates. Communications on Pure & Applied Analysis, 2020, 19 (12) : 54875508. doi: 10.3934/cpaa.2020249 
[5] 
Touria Karite, Ali Boutoulout. Global and regional constrained controllability for distributed parabolic linear systems: RHum approach. Numerical Algebra, Control & Optimization, 2020 doi: 10.3934/naco.2020055 
[6] 
Gongbao Li, Tao Yang. Improved Sobolev inequalities involving weighted Morrey norms and the existence of nontrivial solutions to doubly critical elliptic systems involving fractional Laplacian and Hardy terms. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020469 
[7] 
Shenglan Xie, Maoan Han, Peng Zhu. A posteriori error estimate of weak Galerkin fem for second order elliptic problem with mixed boundary condition. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020340 
[8] 
Jun Zhou. Lifespan of solutions to a fourth order parabolic PDE involving the Hessian modeling epitaxial growth. Communications on Pure & Applied Analysis, 2020, 19 (12) : 55815590. doi: 10.3934/cpaa.2020252 
[9] 
Gunther Uhlmann, Jian Zhai. Inverse problems for nonlinear hyperbolic equations. Discrete & Continuous Dynamical Systems  A, 2021, 41 (1) : 455469. doi: 10.3934/dcds.2020380 
[10] 
Thomas Bartsch, Tian Xu. Strongly localized semiclassical states for nonlinear Dirac equations. Discrete & Continuous Dynamical Systems  A, 2021, 41 (1) : 2960. doi: 10.3934/dcds.2020297 
[11] 
Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reactiondiffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020321 
[12] 
Xuefei He, Kun Wang, Liwei Xu. Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium. Electronic Research Archive, 2020, 28 (4) : 15031528. doi: 10.3934/era.2020079 
[13] 
Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Kleingordon equation. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020448 
[14] 
Zhiyan Ding, Qin Li, Jianfeng Lu. Ensemble Kalman Inversion for nonlinear problems: Weights, consistency, and variance bounds. Foundations of Data Science, 2020 doi: 10.3934/fods.2020018 
[15] 
Yuxia Guo, Shaolong Peng. A direct method of moving planes for fully nonlinear nonlocal operators and applications. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020462 
[16] 
Scipio Cuccagna, Masaya Maeda. A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020450 
[17] 
Kihoon Seong. Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2020, 19 (12) : 54375473. doi: 10.3934/cpaa.2020247 
[18] 
Maoding Zhen, Binlin Zhang, Vicenţiu D. Rădulescu. Normalized solutions for nonlinear coupled fractional systems: Low and high perturbations in the attractive case. Discrete & Continuous Dynamical Systems  A, 2020 doi: 10.3934/dcds.2020379 
[19] 
Zedong Yang, Guotao Wang, Ravi P. Agarwal, Haiyong Xu. Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020436 
[20] 
Youshan Tao, Michael Winkler. Critical mass for infinitetime blowup in a haptotaxis system with nonlinear zeroorder interaction. Discrete & Continuous Dynamical Systems  A, 2021, 41 (1) : 439454. doi: 10.3934/dcds.2020216 
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