-
Previous Article
Invariant measures for the $3$D Navier-Stokes-Voigt equations and their Navier-Stokes limit
- DCDS Home
- This Issue
-
Next Article
Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation
Generalized eigenvalue problem for totally discontinuous operators
1. | UMR 6086 CNRS. Laboratoire de Mathématiques - Université de Poitiers - SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, BP30179 - 86962 Futuroscope Chasseneuil Cedex, France |
-div→p(δφ i(x,δu/δxi))=Au
on a Banach-Sobolev function space V→p and we study the generalized eigenvalue problem Au=λδj(u). Here δφ i (resp. δj) denotes the subdifferential in the sense of convex analysis or more generally in the sense of H. Clarke.
[1] |
Dorota Bors. Application of Mountain Pass Theorem to superlinear equations with fractional Laplacian controlled by distributed parameters and boundary data. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 29-43. doi: 10.3934/dcdsb.2018003 |
[2] |
Ian Schindler, Kyril Tintarev. Mountain pass solutions to semilinear problems with critical nonlinearity. Conference Publications, 2007, 2007 (Special) : 912-919. doi: 10.3934/proc.2007.2007.912 |
[3] |
Dmitry Glotov, P. J. McKenna. Numerical mountain pass solutions of Ginzburg-Landau type equations. Communications on Pure and Applied Analysis, 2008, 7 (6) : 1345-1359. doi: 10.3934/cpaa.2008.7.1345 |
[4] |
Claudianor O. Alves, Giovany M. Figueiredo, Marcelo F. Furtado. Multiplicity of solutions for elliptic systems via local Mountain Pass method. Communications on Pure and Applied Analysis, 2009, 8 (6) : 1745-1758. doi: 10.3934/cpaa.2009.8.1745 |
[5] |
Christopher Grumiau, Marco Squassina, Christophe Troestler. On the Mountain-Pass algorithm for the quasi-linear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1345-1360. doi: 10.3934/dcdsb.2013.18.1345 |
[6] |
Andi Kivinukk, Anna Saksa. On Rogosinski-type approximation processes in Banach space using the framework of the cosine operator function. Mathematical Foundations of Computing, 2022, 5 (3) : 197-218. doi: 10.3934/mfc.2021030 |
[7] |
Noboru Okazawa, Tomomi Yokota. Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 311-341. doi: 10.3934/dcds.2010.28.311 |
[8] |
Sophie Guillaume. Evolution equations governed by the subdifferential of a convex composite function in finite dimensional spaces. Discrete and Continuous Dynamical Systems, 1996, 2 (1) : 23-52. doi: 10.3934/dcds.1996.2.23 |
[9] |
Genady Ya. Grabarnik, Misha Guysinsky. Livšic theorem for banach rings. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4379-4390. doi: 10.3934/dcds.2017187 |
[10] |
Hari Bercovici, Viorel Niţică. A Banach algebra version of the Livsic theorem. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 523-534. doi: 10.3934/dcds.1998.4.523 |
[11] |
Luc Robbiano. Counting function for interior transmission eigenvalues. Mathematical Control and Related Fields, 2016, 6 (1) : 167-183. doi: 10.3934/mcrf.2016.6.167 |
[12] |
Todd Kapitula, Björn Sandstede. Eigenvalues and resonances using the Evans function. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 857-869. doi: 10.3934/dcds.2004.10.857 |
[13] |
Cecilia González-Tokman, Anthony Quas. A concise proof of the multiplicative ergodic theorem on Banach spaces. Journal of Modern Dynamics, 2015, 9: 237-255. doi: 10.3934/jmd.2015.9.237 |
[14] |
Nguyen Thi Toan. Generalized Clarke epiderivatives of the extremum multifunction to a multi-objective parametric discrete optimal control problem. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2705-2720. doi: 10.3934/jimo.2021088 |
[15] |
A. M. Micheletti, Angela Pistoia. Multiple eigenvalues of the Laplace-Beltrami operator and deformation of the Riemannian metric. Discrete and Continuous Dynamical Systems, 1998, 4 (4) : 709-720. doi: 10.3934/dcds.1998.4.709 |
[16] |
Alex Blumenthal. A volume-based approach to the multiplicative ergodic theorem on Banach spaces. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2377-2403. doi: 10.3934/dcds.2016.36.2377 |
[17] |
Raffaele Chiappinelli. Eigenvalues of homogeneous gradient mappings in Hilbert space and the Birkoff-Kellogg theorem. Conference Publications, 2007, 2007 (Special) : 260-268. doi: 10.3934/proc.2007.2007.260 |
[18] |
Benoît Pausader, Walter A. Strauss. Analyticity of the nonlinear scattering operator. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 617-626. doi: 10.3934/dcds.2009.25.617 |
[19] |
Sébastien Gadat, Laurent Miclo. Spectral decompositions and $\mathbb{L}^2$-operator norms of toy hypocoercive semi-groups. Kinetic and Related Models, 2013, 6 (2) : 317-372. doi: 10.3934/krm.2013.6.317 |
[20] |
Myeongju Chae, Soonsik Kwon. The stability of nonlinear Schrödinger equations with a potential in high Sobolev norms revisited. Communications on Pure and Applied Analysis, 2016, 15 (2) : 341-365. doi: 10.3934/cpaa.2016.15.341 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]