-
Previous Article
On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points
- DCDS-B Home
- This Issue
-
Next Article
Multiple periodic solutions to a discrete $p^{(k)}$ - Laplacian problem
A global implicit function theorem and its applications to functional equations
| 1. | Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland |
References:
| [1] |
A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381.
doi: 10.1016/0022-1236(73)90051-7. |
| [2] |
M. Cristea, A note on global implicit function theorem, J. Inequal. Pure and Appl., 8 (2007), 15 pp. |
| [3] |
D. Idczak, A. Skowron and S. Walczak, On the diffeomorphisms between Banach and Hilbert spaces, Advanced Nonlinear Studies, 12 (2012), 89-100. |
| [4] |
A. D. Ioffe and V. M. Tikhomirov, Theory of Extremum Problems, North-Holland, 1979. |
| [5] |
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Amer. Math. Soc., Providence, 1986. |
| [6] |
W. C. Rheinboldt, Local mapping relations and global implicit function theorems, Trans. Amer. Math. Soc., 138 (1969), 183-198.
doi: 10.1090/S0002-9947-1969-0240644-0. |
| [7] |
M. Willem, Minimax Theorems, Birkhauser, Boston, 1996.
doi: 10.1007/978-1-4612-4146-1. |
| [8] |
W. Zhang and S. S. Ge, A Global Implicit Function Theorem without initial point and its applications to control of non-affine systems of high dimensions, J. Math. Anal. Appl, 313 (2006), 251-261.
doi: 10.1016/j.jmaa.2005.08.072. |
show all references
References:
| [1] |
A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381.
doi: 10.1016/0022-1236(73)90051-7. |
| [2] |
M. Cristea, A note on global implicit function theorem, J. Inequal. Pure and Appl., 8 (2007), 15 pp. |
| [3] |
D. Idczak, A. Skowron and S. Walczak, On the diffeomorphisms between Banach and Hilbert spaces, Advanced Nonlinear Studies, 12 (2012), 89-100. |
| [4] |
A. D. Ioffe and V. M. Tikhomirov, Theory of Extremum Problems, North-Holland, 1979. |
| [5] |
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Amer. Math. Soc., Providence, 1986. |
| [6] |
W. C. Rheinboldt, Local mapping relations and global implicit function theorems, Trans. Amer. Math. Soc., 138 (1969), 183-198.
doi: 10.1090/S0002-9947-1969-0240644-0. |
| [7] |
M. Willem, Minimax Theorems, Birkhauser, Boston, 1996.
doi: 10.1007/978-1-4612-4146-1. |
| [8] |
W. Zhang and S. S. Ge, A Global Implicit Function Theorem without initial point and its applications to control of non-affine systems of high dimensions, J. Math. Anal. Appl, 313 (2006), 251-261.
doi: 10.1016/j.jmaa.2005.08.072. |
| [1] |
Antonio Azzollini. On a functional satisfying a weak Palais-Smale condition. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1829-1840. doi: 10.3934/dcds.2014.34.1829 |
| [2] |
Scott Nollet, Frederico Xavier. Global inversion via the Palais-Smale condition. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 17-28. doi: 10.3934/dcds.2002.8.17 |
| [3] |
A. Azzollini. Erratum to: "On a functional satisfying a weak Palais-Smale condition". Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4987-4987. doi: 10.3934/dcds.2014.34.4987 |
| [4] |
Walter Allegretto, John R. Cannon, Yanping Lin. A parabolic integro-differential equation arising from thermoelastic contact. Discrete and Continuous Dynamical Systems, 1997, 3 (2) : 217-234. doi: 10.3934/dcds.1997.3.217 |
| [5] |
Narcisa Apreutesei, Nikolai Bessonov, Vitaly Volpert, Vitali Vougalter. Spatial structures and generalized travelling waves for an integro-differential equation. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 537-557. doi: 10.3934/dcdsb.2010.13.537 |
| [6] |
Shihchung Chiang. Numerical optimal unbounded control with a singular integro-differential equation as a constraint. Conference Publications, 2013, 2013 (special) : 129-137. doi: 10.3934/proc.2013.2013.129 |
| [7] |
Frederic Abergel, Remi Tachet. A nonlinear partial integro-differential equation from mathematical finance. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 907-917. doi: 10.3934/dcds.2010.27.907 |
| [8] |
Samir K. Bhowmik, Dugald B. Duncan, Michael Grinfeld, Gabriel J. Lord. Finite to infinite steady state solutions, bifurcations of an integro-differential equation. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 57-71. doi: 10.3934/dcdsb.2011.16.57 |
| [9] |
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 |
| [10] |
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 |
| [11] |
Giuseppe Maria Coclite, Mario Michele Coclite. Positive solutions of an integro-differential equation in all space with singular nonlinear term. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 885-907. doi: 10.3934/dcds.2008.22.885 |
| [12] |
Miloud Moussai. Application of the bernstein polynomials for solving the nonlinear fractional type Volterra integro-differential equation with caputo fractional derivatives. Numerical Algebra, Control and Optimization, 2022, 12 (3) : 551-568. doi: 10.3934/naco.2021021 |
| [13] |
Michel Chipot, Senoussi Guesmia. On a class of integro-differential problems. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1249-1262. doi: 10.3934/cpaa.2010.9.1249 |
| [14] |
Farid Tari. Geometric properties of the integral curves of an implicit differential equation. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 349-364. doi: 10.3934/dcds.2007.17.349 |
| [15] |
Ankit Kumar, Kamal Jeet, Ramesh Kumar Vats. Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space. Evolution Equations and Control Theory, 2022, 11 (2) : 605-619. doi: 10.3934/eect.2021016 |
| [16] |
Olivier Bonnefon, Jérôme Coville, Jimmy Garnier, Lionel Roques. Inside dynamics of solutions of integro-differential equations. Discrete and Continuous Dynamical Systems - B, 2014, 19 (10) : 3057-3085. doi: 10.3934/dcdsb.2014.19.3057 |
| [17] |
Nestor Guillen, Russell W. Schwab. Neumann homogenization via integro-differential operators. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3677-3703. doi: 10.3934/dcds.2016.36.3677 |
| [18] |
Paola Loreti, Daniela Sforza. Observability of $N$-dimensional integro-differential systems. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 745-757. doi: 10.3934/dcdss.2016026 |
| [19] |
Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Singular integro-differential equations with applications. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021051 |
| [20] |
Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Inverse problems on degenerate integro-differential equations. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022025 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]