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A global inversion theorem for functions with singular points
Podhalańska Państwowa Wyższa Szkoła Zawodowa w Nowym Targu, ul. Kokoszków 71, 34-400 Nowy Targ, Poland |
In this paper, we consider a certain theorem on the global invertibility of a $C^{2n+1}$-mapping between Banach spaces with a singular point in which the derivatives of order up to $2n$ vanish. The theorem is illustrated by several applications.
References:
[1] |
P. Fijałkowski,
Local inversion theorem for singular points, Nonlinear Anal., 54 (2003), 341-349.
doi: 10.1016/S0362-546X(03)00066-X. |
[2] |
P. Fijałkowski,
On a Certain Class of Locally Invertible Mapping and Their Applications, Wydawnictwo Uniwersytetu Lódzkiego, Lódź, 2003. |
[3] |
M. Galewski and M. Rădulescu, On a global implicit function theorem for locally Lipschitz maps via nonsmooth critical point theory, preprint, arXiv: 1704.04280. |
[4] |
O. Gutú, On global inverse and implicit functions, preprint, arXiv: 1508.07028. |
[5] |
J. Hadamard,
Sur les transformations ponctuelles, Bull. Soc. Math. France, 34 (1906), 71-84.
|
[6] |
L. Hörmander,
The Analysis of Linear Partial Differential Operators, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983. |
[7] |
D. Idczak, A. Skowron and S. Walczak,
On the diffeomorphisms between Banach and Hilbert spaces, Adv. Nonlinear Stud., 12 (2012), 89-100.
doi: 10.1515/ans-2012-0105. |
[8] |
G. Katriel,
Mountain pass theorems and global homeomorphism theorems, Annales de l'I. H. P., 11 (1994), 189-209.
doi: 10.1016/S0294-1449(16)30191-3. |
[9] |
R. Plastock,
Homeomorphisms between Banach spaces, Trans. Amer. Math. Soc., 200 (1974), 169-183.
doi: 10.1090/S0002-9947-1974-0356122-6. |
[10] |
M. Rădulescu and S. Rădulescu,
Global inversion theorems and applications to differential equations, Nonlinear Anal., 4 (1980), 951-965.
doi: 10.1016/0362-546X(80)90007-3. |
[11] |
M. Rădulescu and S. Rădulescu,
An application of Hadamard-Levy's theorem to a scalar initial value problem, Proc. Amer. Math. Soc., 106 (1989), 139-143.
doi: 10.2307/2047385. |
[12] |
G. Zampieri,
Diffeomorphisms with Banach space domains, Nonlinear Anal., 19 (1992), 923-932.
doi: 10.1016/0362-546X(92)90104-M. |
show all references
References:
[1] |
P. Fijałkowski,
Local inversion theorem for singular points, Nonlinear Anal., 54 (2003), 341-349.
doi: 10.1016/S0362-546X(03)00066-X. |
[2] |
P. Fijałkowski,
On a Certain Class of Locally Invertible Mapping and Their Applications, Wydawnictwo Uniwersytetu Lódzkiego, Lódź, 2003. |
[3] |
M. Galewski and M. Rădulescu, On a global implicit function theorem for locally Lipschitz maps via nonsmooth critical point theory, preprint, arXiv: 1704.04280. |
[4] |
O. Gutú, On global inverse and implicit functions, preprint, arXiv: 1508.07028. |
[5] |
J. Hadamard,
Sur les transformations ponctuelles, Bull. Soc. Math. France, 34 (1906), 71-84.
|
[6] |
L. Hörmander,
The Analysis of Linear Partial Differential Operators, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983. |
[7] |
D. Idczak, A. Skowron and S. Walczak,
On the diffeomorphisms between Banach and Hilbert spaces, Adv. Nonlinear Stud., 12 (2012), 89-100.
doi: 10.1515/ans-2012-0105. |
[8] |
G. Katriel,
Mountain pass theorems and global homeomorphism theorems, Annales de l'I. H. P., 11 (1994), 189-209.
doi: 10.1016/S0294-1449(16)30191-3. |
[9] |
R. Plastock,
Homeomorphisms between Banach spaces, Trans. Amer. Math. Soc., 200 (1974), 169-183.
doi: 10.1090/S0002-9947-1974-0356122-6. |
[10] |
M. Rădulescu and S. Rădulescu,
Global inversion theorems and applications to differential equations, Nonlinear Anal., 4 (1980), 951-965.
doi: 10.1016/0362-546X(80)90007-3. |
[11] |
M. Rădulescu and S. Rădulescu,
An application of Hadamard-Levy's theorem to a scalar initial value problem, Proc. Amer. Math. Soc., 106 (1989), 139-143.
doi: 10.2307/2047385. |
[12] |
G. Zampieri,
Diffeomorphisms with Banach space domains, Nonlinear Anal., 19 (1992), 923-932.
doi: 10.1016/0362-546X(92)90104-M. |
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