Most cited papers in Differential Equations and Boundary Problems
What are the most cited papers in Differential Equations and Boundary Problems?
The most cited paper in Differential Equations and Boundary Problems is "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators" (Cornelius Lanczos, 1950), with 4,448 citations. Next come "Compact sets in the spaceL p (O,T; B)" (4,138) and "Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I" (3,784).
Showing 50 of 99 papers. Every paper with more than 393 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | An iteration method for the solution of the eigenvalue problem of linear differential and integral operators Cornelius Lanczos · Journal of research of the National Bureau of Standards | Oct 1950 | 4,448 |
| 2 | Compact sets in the spaceL p (O,T; B) Jacques Simon · Annali di Matematica Pura ed Applicata (1923 -) | Dec 1986 | 4,138 |
| 3 | Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I Shmuel Agmon, Avron Douglis, Louis Nirenberg · Communications on Pure and Applied Mathematics | Nov 1959 | 3,784 |
| 4 | Difference Methods for Initial-Value Problems Robert D. Richtmyer, E. H. Dill · Physics Today | Apr 1959 | 3,233 |
| 5 | Ordinary differential equations, transport theory and Sobolev spaces Ronald J. DiPerna, Pierre Louis Lions · Inventiones mathematicae | Oct 1989 | 2,007 |
| 6 | Existence of solitary waves in higher dimensions Walter A. Strauss · Communications in Mathematical Physics | Jun 1977 | 1,834 |
| 7 | On a quasi-linear parabolic equation occurring in aerodynamics Julian D. Cole · Quarterly of Applied Mathematics | Oct 1951 | 1,765 |
| 8 | Weighted norm inequalities for the Hardy maximal function Benjamin Muckenhoupt · Transactions of the American Mathematical Society | 1972 | 1,738 |
| 9 | Regularity for a more general class of quasilinear elliptic equations Peter Tolksdorf · Journal of Differential Equations | 1984 | 1,541 |
| 10 | Rapid solution of integral equations of classical potential theory Vladimir Abramovich Rokhlin · Journal of Computational Physics | Sep 1985 | 1,422 |
| 11 | Elliptic Partial Differential Equations of Second Order Piero Bassanini, Alan R. Elcrat | 1997 | 1,379 |
| 12 | The Theory of Difference Schemes ALEXANDER A. SAMARSKII, VD Radulescu, · Applied Mechanics Reviews | 29 Mar 2001 | 1,220 |
| 13 | Machine contouring using minimum curvature Ian Briggs · Geophysics | Feb 1974 | 1,170 |
| 14 | Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems Antonio Ambrosetti, Haïm Brézis, G. Cerami · Journal of Functional Analysis | Jun 1994 | 1,083 |
| 15 | Quasilinear elliptic-parabolic differential equations Hans Wilhelm Alt, Stephan Luckhaus · Mathematische Zeitschrift | Sep 1983 | 1,055 |
| 16 | Local behavior of solutions of quasi-linear equations James B Serrin · Acta Mathematica | 1964 | 1,033 |
| 17 | On some non-linear elliptic differential-functional equations Philip E. Hartman, Guido Stampacchia · Acta Mathematica | 1966 | 1,005 |
| 18 | NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE Felix E. Browder · Proceedings of the National Academy of Sciences | Oct 1965 | 966 |
| 19 | 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 |
| 20 | The Cauchy problem for quasi-linear symmetric hyperbolic systems Tosio Kato · Archive for Rational Mechanics and Analysis | 1975 | 934 |
| 21 | A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS Henry P. McKean · Proceedings of the National Academy of Sciences | Dec 1966 | 888 |
| 22 | The Inhomogeneous Dirichlet Problem in Lipschitz Domains David S Jerison, Carlos E. Kenig · Journal of Functional Analysis | May 1995 | 864 |
| 23 | Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains Gregory C. Verchota · Journal of Functional Analysis | Dec 1984 | 836 |
| 24 | Bifurcation, perturbation of simple eigenvalues, itand linearized stability Michael G. Crandall, Paul H. Rabinowitz · Archive for Rational Mechanics and Analysis | Jun 1973 | 832 |
| 25 | Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids Akitaka Matsumura, Takaaki Nishida · Communications in Mathematical Physics | Dec 1983 | 832 |
| 26 | 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 |
| 27 | Quasilinear Dirichlet problems driven by positive sources D. D. Joseph, T. S. Lundgren · Archive for Rational Mechanics and Analysis | 1973 | 801 |
| 28 | On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equations Mark Adler · Inventiones mathematicae | Oct 1978 | 793 |
| 29 | L2 estimates and existence theorems for the $\bar \partial $ operator Lars Hörmander · Acta Mathematica | 1965 | 780 |
| 30 | Certain subclasses of analytic and bi-univalent functions H. M. Srivastava, Akshaya Kumar Mishra, P. Gochhayat · Applied Mathematics Letters | 28 May 2010 | 739 |
| 31 | On a dirichlet problem with a singular nonlinearity Michael G. Crandall, Paul H. Rabinowitz, Luc C. Tartar · Communications in Partial Differential Equations | 1977 | 719 |
| 32 | COMPUTATION OF COMBINED REFRACTION - DIFFRACTION J.C.W. Berkhoff · Coastal Engineering Proceedings | 29 Jan 1972 | 717 |
| 33 | Operator–valued Fourier multiplier theorems and maximal $L_p$-regularity Lutz W. Weis · Mathematische Annalen | Apr 2001 | 703 |
| 34 | Nonhomogeneous Linear and Quasilinear Elliptic and Parabolic Boundary Value Problems Herbert Amann · Teubner-Texte zur Mathematik | 1993 | 700 |
| 35 | Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems Carlos E. Kenig · Regional conference series in mathematics | 7 Jul 1994 | 697 |
| 36 | R-Boundedness, Fourier Multipliers, and Problems of Elliptic and Parabolic Type Robert Denk, Matthias Hieber, Jan W. Prüss | Nov 2003 | 689 |
| 37 | On the concept of solution for fractional differential equations with uncertainty Ravi P. Agarwal, Vangipuram Lakshmikantham, Juan J. Nieto · Nonlinear Analysis | 18 Nov 2009 | 686 |
| 38 | Initial value problems in discrete fractional calculus Ferhan Merdivenci Atici, Paul W. Eloe · Proceedings of the American Mathematical Society | 10 Sep 2008 | 682 |
| 39 | Hardy's inequality with weights Benjamin Muckenhoupt · Studia Mathematica | 1972 | 671 |
| 40 | Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions Paolo Marcellini · Archive for Rational Mechanics and Analysis | Sep 1989 | 666 |
| 41 | Ordinary Differential Equations Serge Lang · Undergraduate texts in mathematics | 1983 | 659 |
| 42 | Positive solutions of nonlinear problems involving the square root of the Laplacian Xavier Cabré, Jinggang Tan · Advances in Mathematics | 21 Feb 2010 | 649 |
| 43 | Introduction to H[p] spaces Paul Koosis · Andalas University Repository (Andalas University) | 1998 | 639 |
| 44 | Solutions of Hartree-Fock equations for Coulomb systems Pierre Louis Lions · Communications in Mathematical Physics | Mar 1987 | 627 |
| 45 | Differential equations with discontinuous right-hand sides Shouchuan Hu · Journal of Mathematical Analysis and Applications | 1991 | 615 |
| 46 | Exponential Integrability and Transportation Cost Related to Logarithmic Sobolev Inequalities Sergey G. Bobkov, Friedrich Götze · Journal of Functional Analysis | Apr 1999 | 595 |
| 47 | Boundary behavior of harmonic functions in non-tangentially accessible domains David S Jerison, Carlos E. Kenig · Advances in Mathematics | Oct 1982 | 592 |
| 48 | On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems Shmuel Agmon · Communications on Pure and Applied Mathematics | 1962 | 591 |
| 49 | LPBounds of solutions of reaction-diffusion equations Nicholas D. Alikakos · Communications in Partial Differential Equations | 1979 | 583 |
| 50 | On the Cahn-Hilliard equation Charles M. Elliott, Songmu Zheng · Archive for Rational Mechanics and Analysis | Dec 1986 | 583 |
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.