IPM Positions

Senior Associate Researcher, School of Mathematics (2023 - Present (from March 21, 2023))

Past IPM Positions

Resident Researcher, School of Mathematics (2008 - 2017) Associate Researcher (non-resident), School of Mathematics (2006 - 2008) (Until June ) Associate Researcher, School of Mathematics (2003 - 2006) Associate Researcher (non-resident), School of Mathematics (2001 - 2003)

Non IPM Affiliations

Professor of Imam Khomeini International University

Research Interests

Study of some classes of elliptic operators in the graded Lie groups.

Awards

In the list of the World’s Top 2% Scientists (2022 and 2023)

Research Activities

We study the existence and smoothness of solutions for various types of elliptic operators, including both anisotropic and isotropic versions of the p-Laplacian, specifically on the Heisenberg group as a representative of graded Lie groups. By delving into the existence and regularity of solutions for these elliptic operators, a deeper understanding of their behavior and implications can be gained, contributing to the broader field of mathematical analysis and differential equations. Keywords: p-Laplacian, Heisenberg group, graded Lie groups, weak solution, quasilinear elliptic equation, variational methods AMS subject classifications: 35R03, 35J20, 35J25, 35J62, 35J70, 35B08, 35B09, 35D30

Present Research Project at IPM

The Existence of Solutions for Kohn-Spencer Laplace Equation on Heisenberg Groups

Related Papers

1.	A. Razani (Joint with E. Sengelen Sevim) Traveling Wave Solution for a Hyperbolic Differential Equation Lobachevskii J. Math. 45 (2024), 2932-2944  [abstract]

2.	A. Razani (Joint with G. M. Figueiredo) Positive solutions for semipositon $\Phi$-Laplacian involving nonlocal term in Orlicz-Sobolev space Differential and Integral Equations (Accepted) [abstract]

3.	A. Razani and M.R. Mokhtarzadeh (Joint with Z. Goodarzi) A periodic solution of the coupled matrix Riccati differential equations Miskolc Math. Notes 20 (2019), 887-898  [abstract]

4.	A. Razani (Joint with M. Yazdi) Viscosity approximation method for equilibrium and fixed point problems Fixed Point Theory 14 (2013), 455-472  [abstract]

5.	A. Razani (Joint with F. Khojasteh) Fixed-point theorems for single-valued and multi-valued mixed monotone operators of Meir-Keeler type Journal of Nonlinear and Convex Analysis 14 (2013), 343-350  [abstract]

6.	A. Razani (Joint with S. Homaei Pour, E. Nabizadeh, and M. Beyg Mohamadi) A new version of the Ciric quasi-contraction principle in the modular space NSJOM 43 (2013), 1-9  [abstract]

7.	A. Razani (Joint with S. M. Khalkhali and Sh. Heidarkhani) Infinitely many solutions for a fourth-order boundary-value problem Electron. J. Differential Equations 2012 (2012), 1-14  [abstract]

8.	A. Razani (Joint with M. Yazdi) A new iterative method for generalized equilibrum and fixed point problems of nonexpansive mappings Bull. Malaysian Math. Soc. 35 (2012), 1049-1061  [abstract]

9.	A. Razani Structure of shock wave for a viscous combustion model Filomat 26 (2012), 389-395  [abstract]

10.	M. R. Mokhtarzadeh and A. Razani (Joint with M. R. Pournaki) An existence-uniqueness theorem for a class of boundary value problems Fixed Point Theory 13 (2012), 583-592  [abstract]

11.	A. Razani (Joint with S. Homaeipour) Weak and strong convergence theorems for relatively nonexpansive multi-valued mappings in Banach spaces Fixed Point Theory and Applications 73 (2011), #P9  [abstract]

12.	A. Razani (Joint with S. Homaeipour) Strong convergence theorems of three-step iterations for multi-valued mappings in Banach spaces Filomat 25 (2011), 173-184  [abstract]

13.	A. Razani (Joint with H. Salahifard) Approximating fixed point of generalized nonexpansive mappings Bull. Iranian Math. Soc. 37 (2011), 235-246  [abstract]

14.	A. Razani (joint with S. Homaeipour) Viscosity approximation to common fixed points of families of nonexpansive mappings with weakly contractive mappings Fixed Point Theory and Applications (2010), DOI: 10.1155/2010/476913  [abstract]

15.	A. Razani (Joint with F. Khojasteh and Z. Goodarzi) Some fixed point theorems of integral type contraction in cone metric spaces Fixed Point Theory and Applications 2010 (2010), ID 189684, 13 pages  [abstract]

16.	A. Razani (Joint with V. Rakocevic and Z. Goodarzi) Non-self mappings in modular spaces and common fixed point theorems Cent. Eur. J. Math. 8 (2010), 357-366  [abstract]

17.	A. Razani (Joint with H. Salahifard) Invariant approximation for CAT(0) spaces Nonlinear Anal. 72 (2010), 2421-2425  [abstract]

18.	M. R. Mokhtarzadeh, M. R. Pournaki and A. Razani A note on periodic solutions of Riccati equations Nonlinear Dynam. 62 (2010), 119-125  [abstract]

19.	A. Razani (Joint with R. Moradi) Common fixed point theorems of integral type in modular spaces Bull. Iranian Math. Soc. 35 (2009), 11-24  [abstract]

20.	A. Razani (Joint with M. Beyg Mohamadi, S. Homaei Pou, and E. Nabizadeh) A new version of Krasnoselskii's fixed point theorem in modular spaces Fixed Point Theory 9 (2008), 533-539  [abstract]

21.	M. R. Pournaki and A. Razani Erratum to: On the existence of periodic solutions for a class of generalized forced Lienard equations [Appl. Math. Lett. 20 (2007), no. 3, 248-254] Appl. Math. Lett. 21 (2008), 880  [abstract]

22.	A. Razani (Joint with E. Nabizadeh, M. Beyg Mohammadi, and S. Homaei Pour) Fixed points of nonlinear and asymptotic contractions in the modular space Abstr. Appl. Anal. 2007 (2007), 10 pages  [abstract]

23.	M. R. Pournaki and A. Razani On the existence of periodic solutions for a class of generalized forced Lienard equations Appl. Math. Lett. 20 (2007), 248-254  [abstract]

24.	A. Razani A fixed point theorem in the Menger probabilistic metric space New Zealand J. Math. 35 (2006), 109-114  [abstract]

25.	M. B. Ghaemi and A. Razani Fixed and periodic points in the probabilistic normed and metric spaces Chaos, Solitons and Fractals 28 (2006), 1181-1187  [abstract]

26.	A. Razani Existence of Chapman-Jouguet detonation for a viscous combustion model J. Math. Anal. Appl. 293 (2004), 551-563  [abstract]

27.	A. Razani On the existence of premixed laminar flames Bull. Aust. Math. Soc. 69 (2004), 415-427  [abstract]

28.	A. Razani Weak and strong detonation profiles for a qualitative model J. Math. Anal. Appl. 276 (2002), 868-881  [abstract]

29.	M. Hesaaraki and A. Razani On the existence of Chapman-Jouguet detonation waves Bull. Aust. Math. Soc. 63 (2001), 485-496  [abstract]

30.	M. Hesaaraki and A. Razani Detonative travelling waves for combustions Appl. Anal. 77 (2001), 405-418  [abstract]