Most cited papers in Nonlinear Differential Equations Analysis
What are the most cited papers in Nonlinear Differential Equations Analysis?
The most cited paper in Nonlinear Differential Equations Analysis is "User’s guide to viscosity solutions of second order partial differential equations" (Michael G. Crandall, Hitoshi Ishii, Pierre-Louis Lions, 1992), with 5,020 citations. Next come "Dual variational methods in critical point theory and applications" (4,419) and "A new definition of fractional derivative" (3,504).
Showing 50 of 100 papers. Every paper with more than 485 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | User’s guide to viscosity solutions of second order partial differential equations Michael G. Crandall, Hitoshi Ishii, Pierre-Louis Lions · Bulletin of the American Mathematical Society | 1992 | 5,020 |
| 2 | Dual variational methods in critical point theory and applications Antonio Ambrosetti, Paul H. Rabinowitz · Journal of Functional Analysis | Dec 1973 | 4,419 |
| 3 | A new definition of fractional derivative Roshdi Rashid Khalil, Mohammed Al Horani, A. Yousef et al. · Journal of Computational and Applied Mathematics | 16 Jan 2014 | 3,504 |
| 4 | Positive solutions of nonlinear elliptic equations involving critical sobolev exponents Haïm Brézis, Louis Nirenberg · Communications on Pure and Applied Mathematics | Jul 1983 | 2,942 |
| 5 | Symmetry and related properties via the maximum principle Basilis Gidas, Wei‐Ming Ni, Louis Nirenberg · Communications in Mathematical Physics | Oct 1979 | 2,934 |
| 6 | An Extension Problem Related to the Fractional Laplacian Luis Caffarelli, Luis Silvestre · Communications in Partial Differential Equations | 8 Aug 2007 | 2,342 |
| 7 | An extension problem related to the fractional Laplacian Luis A. Caffarelli, Luís Silvestre | 2006 | 2,125 |
| 8 | A relation between pointwise convergence of functions and convergence of functionals Haïm Brézis, Élliott H. Lieb · Proceedings of the American Mathematical Society | Jul 1983 | 2,089 |
| 9 | On conformable fractional calculus Thabet Abdeljawad · Journal of Computational and Applied Mathematics | 29 Oct 2014 | 2,054 |
| 10 | Some global results for nonlinear eigenvalue problems Paul H. Rabinowitz · Journal of Functional Analysis | Jun 1971 | 1,896 |
| 11 | Finite difference/spectral approximations for the time-fractional diffusion equation Yumin Lin, Chuanju Xu · Journal of Computational Physics | 15 Feb 2007 | 1,843 |
| 12 | A new collection of real world applications of fractional calculus in science and engineering HongGuang Sun, Yong Zhang, Dumitru Bǎleanu et al. · Communications in Nonlinear Science and Numerical Simulation | 24 Apr 2018 | 1,786 |
| 13 | Stability results for fractional differential equations with applications to control processing Denis Matignon | 1996 | 1,442 |
| 14 | Uniqueness of positive solutions of Δu−u+up=0 in Rn Man Kam Kwong · Archive for Rational Mechanics and Analysis | Sep 1989 | 1,352 |
| 15 | A Caputo fractional derivative of a function with respect to another function Ricardo Almeida · Communications in Nonlinear Science and Numerical Simulation | 12 Sep 2016 | 1,283 |
| 16 | Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations Juan J. Nieto, Rosana Rodríguez‐López · Order | Aug 2005 | 1,261 |
| 17 | The approach of solutions of nonlinear diffusion equations to travelling front solutions Paul C. Fife, J. Bryce McLeod · Archive for Rational Mechanics and Analysis | Dec 1977 | 1,177 |
| 18 | Basic theory of fractional differential equations Vangipuram Lakshmikantham, Aghalaya S. Vatsala · Nonlinear Analysis | 28 Aug 2007 | 1,140 |
| 19 | Positive solutions for boundary value problem of nonlinear fractional differential equation Zhanbing Bai, Haishen Lü · Journal of Mathematical Analysis and Applications | 11 Apr 2005 | 1,102 |
| 20 | Construction of fixed points of nonlinear mappings in Hilbert space Felix E. Browder, W. V. Petryshyn · Journal of Mathematical Analysis and Applications | Nov 1967 | 1,030 |
| 21 | A generalized Gronwall inequality and its application to a fractional differential equation Haiping Ye, Jianming Gao, Yongsheng Ding · Journal of Mathematical Analysis and Applications | 7 Jul 2006 | 1,027 |
| 22 | Generalized Taylor’s formula Zaid Odibat, Nabil T. Shawagfeh · Applied Mathematics and Computation | 12 Sep 2006 | 972 |
| 23 | Finite difference approximations for two-sided space-fractional partial differential equations Mark M. Meerschaert, Charles Tadjeran · Applied Numerical Mathematics | 18 Mar 2005 | 952 |
| 24 | Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem Ludwik Byszewski · Journal of Mathematical Analysis and Applications | Dec 1991 | 939 |
| 25 | A fixed point theorem for asymptotically nonexpansive mappings K. Goebel, W. A. Kirk · Proceedings of the American Mathematical Society | Sep 1972 | 912 |
| 26 | A new difference scheme for the time fractional diffusion equation Anatoly A. Alikhanov · Journal of Computational Physics | 4 Oct 2014 | 898 |
| 27 | On the fuzzy initial value problem Seppo Seikkala · Fuzzy Sets and Systems | Dec 1987 | 888 |
| 28 | Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order Abdon Atangana, İlknur Koca · Chaos Solitons & Fractals | 8 Mar 2016 | 871 |
| 29 | The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary Xavier Ros‐Oton, Joaquim Serra · Journal de Mathématiques Pures et Appliquées | 13 Jun 2013 | 870 |
| 30 | On the ψ -Hilfer fractional derivative J. Vanterler da C. Sousa, Edmundo Capelas de Oliveira · Communications in Nonlinear Science and Numerical Simulation | 9 Jan 2018 | 860 |
| 31 | On stability of additive mappings Zbigniew Gajda · International Journal of Mathematics and Mathematical Sciences | 1991 | 859 |
| 32 | On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ N Louis Jeanjean · Proceedings of the Royal Society of Edinburgh Section A Mathematics | 1999 | 858 |
| 33 | Classification of solutions for an integral equation Wenxiong Chen, Congming Li, Biao Ou · Communications on Pure and Applied Mathematics | 19 Dec 2005 | 844 |
| 34 | Nonlinear semigroups and evolution equations Tosio Kato · Journal of the Mathematical Society of Japan | Oct 1967 | 840 |
| 35 | Existence of solutions for p(x)-Laplacian Dirichlet problem Xianling Fan, Qihu Zhang · Nonlinear Analysis | 28 Dec 2002 | 837 |
| 36 | A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions Ravi P. Agarwal, Mouffak Benchohra, Samira Hamani · Acta Applicandae Mathematicae | 10 Nov 2008 | 832 |
| 37 | Regularity and existence of solutions of elliptic equations with p,q-growth conditions Paolo Marcellini · Journal of Differential Equations | Mar 1991 | 826 |
| 38 | A General Formulation and Solution Scheme for Fractional Optimal Control Problems Om P. Agrawal · Nonlinear Dynamics | Dec 2004 | 813 |
| 39 | Existence and multiplicity results for some superlinear elliptic problems on R N Thomas Bartsch, Zhiqiang Wang · Communications in Partial Differential Equations | 1995 | 813 |
| 40 | Orbits of families of vector fields and integrability of distributions Héctor J. Sussmann · Transactions of the American Mathematical Society | 1973 | 788 |
| 41 | A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative Dumitru Bǎleanu, Amin Jajarmi, Hakimeh Mohammadi et al. · Chaos Solitons & Fractals | 25 Feb 2020 | 773 |
| 42 | Weak and strong convergence to fixed points of asymptotically nonexpansive mappings Jürgen Schu · Bulletin of the Australian Mathematical Society | Feb 1991 | 771 |
| 43 | Properties of a New Fractional Derivative without Singular Kernel Jorge Losada, Juan J. Nieto, Saudi Arabia | 2015 | 766 |
| 44 | On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain Abbas Bahri, Jean‐Michel Coron · Communications on Pure and Applied Mathematics | Apr 1988 | 763 |
| 45 | New approach to a generalized fractional integral Udita N. Katugampola · Applied Mathematics and Computation | 15 Apr 2011 | 762 |
| 46 | Asymptotic speeds of spread and traveling waves for monotone semiflows with applications Xing Liang, Xiaoqiang Zhao · Communications on Pure and Applied Mathematics | 9 Aug 2006 | 751 |
| 47 | Inertial manifolds for nonlinear evolutionary equations Ciprian Foiaş, George R. Sell, Roger Témam · Journal of Differential Equations | Jun 1988 | 736 |
| 48 | On Riemann and Caputo fractional differences Thabet Abdeljawad · Computers & Mathematics with Applications | 14 Apr 2011 | 735 |
| 49 | The role of fractional calculus in modeling biological phenomena: A review Clara Mihaela Ionescu, António Mendes Lopes, Dana Copoţ et al. · Communications in Nonlinear Science and Numerical Simulation | 10 Apr 2017 | 732 |
| 50 | One-parameter semigroups E. B. Davies · Cambridge University Press eBooks | 26 Apr 2007 | 724 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.