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Existence and nonexistence results for a class of parabolic equations with mixed boundary conditions
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Lindstedt series for periodic solutions of beam equations with quadratic and velocity dependent nonlinearities
1.  Dipartimento di Matematica, Università di Roma "Tor Vergata", Roma, I00133 
2.  Dipartimento di Matematica, Università di Roma Tre, Roma, I00146, Italy 
[1] 
G. Gentile, V. Mastropietro. Convergence of Lindstedt series for the non linear wave equation. Communications on Pure and Applied Analysis, 2004, 3 (3) : 509514. doi: 10.3934/cpaa.2004.3.509 
[2] 
Koichiro Naito. Recurrent dimensions of quasiperiodic solutions for nonlinear evolution equations II: Gaps of dimensions and Diophantine conditions. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 449488. doi: 10.3934/dcds.2004.11.449 
[3] 
E. Muñoz Garcia, R. PérezMarco. Diophantine conditions in small divisors and transcendental number theory. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 14011409. doi: 10.3934/dcds.2003.9.1401 
[4] 
José M. Arrieta, Simone M. Bruschi. Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a non uniformly Lipschitz deformation. Discrete and Continuous Dynamical Systems  B, 2010, 14 (2) : 327351. doi: 10.3934/dcdsb.2010.14.327 
[5] 
Andrzej Nowakowski. Variational approach to stability of semilinear wave equation with nonlinear boundary conditions. Discrete and Continuous Dynamical Systems  B, 2014, 19 (8) : 26032616. doi: 10.3934/dcdsb.2014.19.2603 
[6] 
Le Thi Phuong Ngoc, Nguyen Thanh Long. Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions. Communications on Pure and Applied Analysis, 2013, 12 (5) : 20012029. doi: 10.3934/cpaa.2013.12.2001 
[7] 
Mariane Bourgoing. Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Existence and applications to the levelset approach. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 10471069. doi: 10.3934/dcds.2008.21.1047 
[8] 
Micol Amar. A note on boundary layer effects in periodic homogenization with Dirichlet boundary conditions. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 537556. doi: 10.3934/dcds.2000.6.537 
[9] 
Le Thi Phuong Ngoc, Khong Thi Thao Uyen, Nguyen Huu Nhan, Nguyen Thanh Long. On a system of nonlinear pseudoparabolic equations with RobinDirichlet boundary conditions. Communications on Pure and Applied Analysis, 2022, 21 (2) : 585623. doi: 10.3934/cpaa.2021190 
[10] 
Vesselin Petkov. Location of eigenvalues for the wave equation with dissipative boundary conditions. Inverse Problems and Imaging, 2016, 10 (4) : 11111139. doi: 10.3934/ipi.2016034 
[11] 
Enzo Vitillaro. Blow–up for the wave equation with hyperbolic dynamical boundary conditions, interior and boundary nonlinear damping and sources. Discrete and Continuous Dynamical Systems  S, 2021, 14 (12) : 45754608. doi: 10.3934/dcdss.2021130 
[12] 
Gennaro Infante. Positive solutions of differential equations with nonlinear boundary conditions. Conference Publications, 2003, 2003 (Special) : 432438. doi: 10.3934/proc.2003.2003.432 
[13] 
Michele V. Bartuccelli, G. Gentile, Kyriakos V. Georgiou. Kam theory, Lindstedt series and the stability of the upsidedown pendulum. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 413426. doi: 10.3934/dcds.2003.9.413 
[14] 
Marc Briant. Perturbative theory for the Boltzmann equation in bounded domains with different boundary conditions. Kinetic and Related Models, 2017, 10 (2) : 329371. doi: 10.3934/krm.2017014 
[15] 
Hugo Beirão da Veiga. A challenging open problem: The inviscid limit under sliptype boundary conditions.. Discrete and Continuous Dynamical Systems  S, 2010, 3 (2) : 231236. doi: 10.3934/dcdss.2010.3.231 
[16] 
Andreas Henrici. Symmetries of the periodic Toda lattice, with an application to normal forms and perturbations of the lattice with Dirichlet boundary conditions. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 29492977. doi: 10.3934/dcds.2015.35.2949 
[17] 
Nicolas Fourrier, Irena Lasiecka. Regularity and stability of a wave equation with a strong damping and dynamic boundary conditions. Evolution Equations and Control Theory, 2013, 2 (4) : 631667. doi: 10.3934/eect.2013.2.631 
[18] 
Guanggan Chen, Jian Zhang. Asymptotic behavior for a stochastic wave equation with dynamical boundary conditions. Discrete and Continuous Dynamical Systems  B, 2012, 17 (5) : 14411453. doi: 10.3934/dcdsb.2012.17.1441 
[19] 
Michael Renardy. A backward uniqueness result for the wave equation with absorbing boundary conditions. Evolution Equations and Control Theory, 2015, 4 (3) : 347353. doi: 10.3934/eect.2015.4.347 
[20] 
Arnaud Heibig, Mohand Moussaoui. Exact controllability of the wave equation for domains with slits and for mixed boundary conditions. Discrete and Continuous Dynamical Systems, 1996, 2 (3) : 367386. doi: 10.3934/dcds.1996.2.367 
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