Nonlinear Partial Differential Equations
Nonlinear Partial Differential Equations is a research topic within Applied Mathematics. Science Explorer counts 25k research works in it since 1956. 17.9% of them reached the world's top 10% most cited for their field and year.
This cluster of papers focuses on the theory of fractional Laplacian operators, including topics such as Sobolev spaces, nonlinear equations, regularity theory, variational problems, critical exponents, ground state solutions, elliptic equations, nonlocal operators, and Hamiltonian estimates.
- Fractional Laplacian
- Sobolev Spaces
- Nonlinear Equations
- Regularity Theory
- Variational Problems
- Critical Exponents
- Ground State Solutions
- Elliptic Equations
- Nonlocal Operators
- Hamiltonian Estimates
- Research works
- 25k fractional, since 1956
- In the world top 10%
- 4.5k per year above
- Top-10% rate
- 17.9% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- +19% the tick is no change
Which countries lead Nonlinear Partial Differential Equations research?
By volume, China and Italy publish the most (1.5k and 377 works in 2022–2025).
How concentrated that is
The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.
Shares of the rows listed above, not of the whole node.
Which institutions lead Nonlinear Partial Differential Equations research?
By volume in 2022–2025, Southwest University publishes the most Nonlinear Partial Differential Equations research, followed by Université Sultan Moulay Slimane and Central South University.
By volume, 2022–2025
- 1 Southwest University China 50 works
- 2 Université Sultan Moulay Slimane Morocco 45 works
- 3 Central South University China 43 works
- 4 Tsinghua University China 39 works
- 5 Beijing Normal University China 37 works
- 6 Sapienza University of Rome Italy 32 works
- 7 Zhejiang Normal University China 29 works
- 8 Centre National de la Recherche Scientifique France 27 works
- 9 Sidi Mohamed Ben Abdellah University Morocco 26 works
- 10 Central China Normal University China 25 works
Who are the leading researchers in Nonlinear Partial Differential Equations?
The most-cited researchers publishing on Nonlinear Partial Differential Equations include Terence Tao, Louis Nirenberg and Élliott H. Lieb.
- 1 Terence Tao 3.1k citations
- 2 Louis Nirenberg 2.9k citations
- 3 Élliott H. Lieb 2.5k citations
- 4 Shing–Tung Yau 2.1k citations
- 5 Xiaodong Wang 2k citations
- 6 Liqun Zhang 2k citations
- 7 Pierre‐Louis Lions 1.7k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Nonlinear Partial Differential Equations research done?
The largest centres of Nonlinear Partial Differential Equations research in 2022–2025 are Beijing (China), Chongqing (China), Shanghai (China) and Wuhan (China). Among places with at least 20 works in it, it is an unusually large share of all research in Beni Mellal and Qazvin.
Largest cities, 2022–2025
Where it is the local speciality
- Beni MellalMA · 44.8 works74×
- QazvinIR · 20.7 works36×
Location quotient: how much more of its research is in Nonlinear Partial Differential Equations than the world average.
Where is the best place to study Nonlinear Partial Differential Equations?
Among universities, judged by research, Marche Polytechnic University, Université Sultan Moulay Slimane and Bielefeld University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Marche Polytechnic University Italy | 76.8 | 53.4% | 13.3× | 11 | +248.6% |
| 2 | Université Sultan Moulay Slimane Morocco | 72.6 | 37.3% | 74.2× | 45 | — |
| 3 | Bielefeld University Germany | 64.7 | 44.0% | 10.9× | 11 | +96.1% |
| 4 | Beijing Normal University China | 64.2 | 29.6% | 12.3× | 37 | +5.9% |
| 5 | Shandong University of Science and Technology China | 62.5 | 22.0% | 9.6× | 21 | +377.2% |
| 6 | Sidi Mohamed Ben Abdellah University Morocco | 62.1 | 13.2% | 21.8× | 26 | +649.5% |
| 7 | Tunis El Manar University Tunisia | 60.9 | 14.8% | 21.2× | 16 | +256.2% |
| 8 | Guangzhou University China | 60.6 | 24.6% | 13.8× | 22 | +82.7% |
| 9 | National Institute for Mathematical Sciences South Korea | 59.9 | 26.6% | 180.9× | 8 | +456.4% |
| 10 | Southwest University China | 58.8 | 12.8% | 21.0× | 50 | +36.8% |
Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.
Is Nonlinear Partial Differential Equations research growing?
Output in 2018–2022 was 19% higher than in 2013–2017, peaking in 2022. The fastest-growing topics are Nonlinear Partial Differential Equations.
The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.
Which topics inside it are moving
Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.