Science Explorer Back to mapMap
Discussion
Topic · Applied Mathematics

Nonlinear Differential Equations Analysis

Nonlinear Differential Equations Analysis is a research topic within Applied Mathematics. Science Explorer counts 28k research works in it since 1950. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the theory and applications of fractional differential equations, covering topics such as boundary value problems, semilinear and impulsive differential equations, existence results, controllability, mild solutions, nonlinear systems, time scales, and functional differential equations.

  • Fractional Differential Equations
  • Boundary Value Problems
  • Semilinear Differential Equations
  • Impulsive Differential Equations
  • Existence Results
  • Controllability
  • Mild Solutions
  • Nonlinear Systems
  • Time Scales
  • Functional Differential Equations
Research works
28k
fractional, since 1950
In the world top 10%
2.8k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+1%
the tick is no change
Largest producer
China
37% of the 10 largest, 2022-now
Nonlinear Differential Equations Analysis

Which countries lead Nonlinear Differential Equations Analysis research?

By volume, China and India publish the most (1.3k and 546 works in 2022-now).

By volume, 2022-now

  1. 1 China 1.3k works
  2. 2 India 546 works
  3. 3 Saudi Arabia 367 works
  4. 4 Algeria 237 works
  5. 5 Türkiye 203 works
  6. 6 United States 191 works
  7. 7 Morocco 188 works
  8. 8 Russia 162 works
  9. 9 Iran 142 works
  10. 10 Italy 138 works

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.

China: 37.0%India: 15.8%Saudi Arabia: 10.6%Algeria: 6.9%6 others listed: 29.6%37%largest
China1,277 · 37.0%India546 · 15.8%Saudi Arabia367 · 10.6%Algeria237 · 6.9%6 others listed1,023 · 29.6%

Shares of the rows listed above, not of the whole node.

Which institutions lead Nonlinear Differential Equations Analysis research?

By volume in 2022-now, Université Sultan Moulay Slimane publishes the most Nonlinear Differential Equations Analysis research, followed by Vellore Institute of Technology University and Northwest Normal University.

By volume, 2022-now

  1. 1 Université Sultan Moulay SlimaneMorocco 67 works
  2. 2 Vellore Institute of Technology UniversityIndia 63 works
  3. 3 Northwest Normal UniversityChina 44 works
  4. 4 King Abdulaziz UniversitySaudi Arabia 44 works
  5. 5 Qassim UniversitySaudi Arabia 42 works
  6. 6 Russian Academy of SciencesRussia 40 works
  7. 7 Centre National de la Recherche ScientifiqueFrance 38 works
  8. 8 University of SfaxTunisia 30 works
  9. 9 Islamic Azad University, TehranIran 30 works
  10. 10 King Saud UniversitySaudi Arabia 28 works

Who are the leading researchers in Nonlinear Differential Equations Analysis?

The most-cited researchers publishing on Nonlinear Differential Equations Analysis include Sudhir Kumar, Tasawar Hayat and Stanley Osher.

  1. 1 Sudhir Kumar United States 295k citations
  2. 2 Tasawar Hayat Pakistan 135k citations
  3. 3 Stanley Osher United States 119k citations
  4. 4 Guanrong Chen China 116k citations
  5. 5 George Em Karniadakis United States 113k citations
  6. 6 Jinde Cao China 104k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

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).

Most cited papers
#PaperReleasedCitations
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 Open access 1992 5,020
2 Dual variational methods in critical point theory and applications Antonio Ambrosetti, Paul H. Rabinowitz · Journal of Functional Analysis Open access 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 Open access 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
All 100 most cited papers, with filters and sorting

Where is Nonlinear Differential Equations Analysis research done?

The largest centres of Nonlinear Differential Equations Analysis research in 2022-now are Riyadh (Saudi Arabia), Beijing (China), Lanzhou (China) and Beni Mellal (Morocco). Among places with at least 20 works in it, it is an unusually large share of all research in Sidi Bel Abbes and Beni Mellal.

Largest cities, 2022-now

  1. 1 RiyadhSaudi Arabia 102 works
  2. 2 BeijingChina 101 works
  3. 3 LanzhouChina 79 works
  4. 4 Beni MellalMorocco 67 works
  5. 5 VelloreIndia 66 works
  6. 6 JeddahSaudi Arabia 62 works
  7. 7 ShanghaiChina 57 works
  8. 8 ChangshaChina 53 works
  9. 9 GuangzhouChina 52 works
  10. 10 GuiyangChina 50 works

Where it is the local speciality

  1. Sidi Bel AbbesDZ · 25.2 works90×
  2. Beni MellalMA · 66.5 works88×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Nonlinear Differential Equations Analysis than the world average.

See Nonlinear Differential Equations Analysis on the map

Where is the best place to study Nonlinear Differential Equations Analysis?

Among universities, judged by research, Vellore Institute of Technology University, Prince Sattam Bin Abdulaziz University and Al-Balqa Applied 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.

0%20%40%mean 28.09%fractional works in this field (log) →share of work in the world top 10% →Al-Balqa Applied Uni…Vellore Institute of…Prince Sattam Bin Ab…Qassim University
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Vellore Institute of Technology UniversityIndia 81.136.6%13.7×63 +330.9%
2Prince Sattam Bin Abdulaziz UniversitySaudi Arabia 69.827.2%22.8×28 +138.0%
3Al-Balqa Applied UniversityJordan 68.243.2%21.5×11 +41.5%
4Qassim UniversitySaudi Arabia 61.614.9%34.9×42 +291.3%
5Prince Sultan UniversitySaudi Arabia 61.524.2%48.2×25 -10.2%
6Université Sultan Moulay SlimaneMorocco 60.611.2%103.5×66 +190.1%
7China Medical UniversityTaiwan 58.627.7%41.5×27 -16.3%
8Lebanese American UniversityLebanon 56.537.6%16.3×8 -
9Bu-Ali Sina UniversityIran 56.142.1%21.5×9 +64.7%
10Princess Nourah bint Abdulrahman UniversitySaudi Arabia 55.916.2%16.9×20 +138.9%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Nonlinear Differential Equations Analysis, country by country

Is Nonlinear Differential Equations Analysis research growing?

Output in 2022-2025 was 1% higher than in 2018-2021, peaking in 2021. The fastest-growing topics are Nonlinear Differential Equations Analysis.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Nonlinear Differential Equations Analysis as a percentage of every work published that year, 0.020% in 2024.

still counting0.020%0.040%Nonlinear Differential Equations Analysis0.020% in 202519801990200020102020

Fractional works of Nonlinear Differential Equations Analysis over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Nonlinear Differential Equations Analysis9.8% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

Discussion

Ask a question or share a note about Nonlinear Differential Equations Analysis. Posts are plain text and can be reported.