# American Institute of Mathematical Sciences

January  2018, 23(1): 173-180. doi: 10.3934/dcdsb.2018011

## 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

Received  July 2016 Revised  May 2017 Published  January 2018

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.

Citation: Piotr Fijałkowski. A global inversion theorem for functions with singular points. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 173-180. doi: 10.3934/dcdsb.2018011
##### References:

show all references

##### References:
 [1] Giuseppe Maria Coclite, Mario Michele Coclite. Positive solutions of an integro-differential equation in all space with singular nonlinear term. Discrete & Continuous Dynamical Systems, 2008, 22 (4) : 885-907. doi: 10.3934/dcds.2008.22.885 [2] 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 [3] Frederic Abergel, Remi Tachet. A nonlinear partial integro-differential equation from mathematical finance. Discrete & Continuous Dynamical Systems, 2010, 27 (3) : 907-917. doi: 10.3934/dcds.2010.27.907 [4] Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Singular integro-differential equations with applications. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021051 [5] Miloud Moussai. Application of the bernstein polynomials for solving the nonlinear fractional type Volterra integro-differential equation with caputo fractional derivatives. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021021 [6] Michel Chipot, Senoussi Guesmia. On a class of integro-differential problems. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1249-1262. doi: 10.3934/cpaa.2010.9.1249 [7] Tonny Paul, A. Anguraj. Existence and uniqueness of nonlinear impulsive integro-differential equations. Discrete & Continuous Dynamical Systems - B, 2006, 6 (5) : 1191-1198. doi: 10.3934/dcdsb.2006.6.1191 [8] Sertan Alkan. A new solution method for nonlinear fractional integro-differential equations. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1065-1077. doi: 10.3934/dcdss.2015.8.1065 [9] Walter Allegretto, John R. Cannon, Yanping Lin. A parabolic integro-differential equation arising from thermoelastic contact. Discrete & Continuous Dynamical Systems, 1997, 3 (2) : 217-234. doi: 10.3934/dcds.1997.3.217 [10] Narcisa Apreutesei, Nikolai Bessonov, Vitaly Volpert, Vitali Vougalter. Spatial structures and generalized travelling waves for an integro-differential equation. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 537-557. doi: 10.3934/dcdsb.2010.13.537 [11] Samir K. Bhowmik, Dugald B. Duncan, Michael Grinfeld, Gabriel J. Lord. Finite to infinite steady state solutions, bifurcations of an integro-differential equation. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 57-71. doi: 10.3934/dcdsb.2011.16.57 [12] Olivier Bonnefon, Jérôme Coville, Jimmy Garnier, Lionel Roques. Inside dynamics of solutions of integro-differential equations. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3057-3085. doi: 10.3934/dcdsb.2014.19.3057 [13] Nestor Guillen, Russell W. Schwab. Neumann homogenization via integro-differential operators. Discrete & Continuous Dynamical Systems, 2016, 36 (7) : 3677-3703. doi: 10.3934/dcds.2016.36.3677 [14] Paola Loreti, Daniela Sforza. Observability of $N$-dimensional integro-differential systems. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 745-757. doi: 10.3934/dcdss.2016026 [15] Elena Bonetti, Elisabetta Rocca. Global existence and long-time behaviour for a singular integro-differential phase-field system. Communications on Pure & Applied Analysis, 2007, 6 (2) : 367-387. doi: 10.3934/cpaa.2007.6.367 [16] Hermann Brunner. The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays. Communications on Pure & Applied Analysis, 2006, 5 (2) : 261-276. doi: 10.3934/cpaa.2006.5.261 [17] Xinjie Dai, Aiguo Xiao, Weiping Bu. Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler–Maruyama approximation. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021225 [18] Jean-Michel Roquejoffre, Juan-Luis Vázquez. Ignition and propagation in an integro-differential model for spherical flames. Discrete & Continuous Dynamical Systems - B, 2002, 2 (3) : 379-387. doi: 10.3934/dcdsb.2002.2.379 [19] Tomás Caraballo, P.E. Kloeden. Non-autonomous attractors for integro-differential evolution equations. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 17-36. doi: 10.3934/dcdss.2009.2.17 [20] Liang Zhang, Bingtuan Li. Traveling wave solutions in an integro-differential competition model. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 417-428. doi: 10.3934/dcdsb.2012.17.417

2020 Impact Factor: 1.327