Differential Equations with Discontinuous Righthand Sides
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For the input quantization case, a Filippov solution P(t) exists and is absolutely continuous on [0,∞), and there exists at least one weak solution u(x,t) ∈ L∞([0,D]×R+;R) for the transport PDE part, yielding a solution X(t) ∈ AC(R+;R^n).
“Thus, a Filippov solution P ( t ) exists (under the local Lipschitzness assumptions on f and κ ) by, e.g., [14], which is absolutely continuous on [0 , ∞ ) .”
From Semiglobal Switched Predictor-Feedback Stabilization of Nonlinear Systems With Input Delay and State/Input Quantization (2026) · cites this paper as [14]
Cited by
Sorted by citations
Sliding Mode Direct Yaw-Moment Control Design for In-Wheel Electric Vehicles
Ding, S., Liu, L., & Zheng, W. X. (2017) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2017.2682024 · Cited by 414 · see citing works
A Robust Observer-Based Sensor Fault-Tolerant Control for PMSM in Electric Vehicles
Kommuri, S. K., Defoort, M., Karimi, H. R., & Veluvolu, K. C. (2016) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2016.2590993 · Cited by 408 · see citing works
Targeted energy transfers in vibro-impact oscillators for seismic mitigation
Nucera, F., Vakakis, A. F., McFarland, D. M., Bergman, L. A., & Kerschen, G. (2007) · Nonlinear Dynamics · doi:10.1007/s11071-006-9189-7 · Cited by 254 · see citing works
Colledanchise, M., & Ogren, P. (2017) · IEEE Transactions on Robotics · doi:10.1109/tro.2016.2633567 · Cited by 209 · see citing works
Second-Order Sliding Mode Control for Nonlinear Uncertain Systems Bounded by Positive Functions
Ding, S., Wang, J., & Zheng, W. X. (2015) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2015.2448064 · Cited by 162 · see citing works
Efficient algorithms for collision avoidance at intersections
Colombo, A., & Del Vecchio, D. (2012) · Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control · doi:10.1145/2185632.2185656 · Cited by 134 · see citing works
A Survey of the Hysteretic Duhem Model
Ikhouane, F. (2018) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-017-9218-3 · Cited by 66 · see citing works
On the coupling of systems of hyperbolic conservation laws with ordinary differential equations
Borsche, R., Colombo, R. M., & Garavello, M. (2010) · Nonlinearity · doi:10.1088/0951-7715/23/11/002 · Cited by 55 · see citing works
Koudohode, F., & Bekiaris-Liberis, N. (2026) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2026.3730335
- Authors
- Filippov, A. F.
- Corresponding author
- Filippov, A. F.
- Venue
- Mathematics and Its Applications
- Publisher
- Springer Netherlands
- Published
- 1988
- ISSN
- 0169-6378 (ISSN-L)
- OpenAlex
- W4293078920
- Cited by
- 4,720
- References
- 0
- Citations by year
- 2026: 145 · 2025: 248 · 2024: 224 · 2023: 269 · 2022: 257 · 2021: 268 · 2020: 268 · 2019: 237 · 2018: 271 · 2017: 296 · 2016: 247 · 2015: 225 · 2014: 192 · 2013: 166 · 2012: 161
- FWCI
- 1.73
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Mathematics and its applications. Soviet series (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Differential Equations Analysis
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Physical Sciences › Mathematics › Applied Mathematics › Differential Equations and Boundary Problems
- Keywords
- differential equations, discontinuous right-hand side, impulsive differential equations, discontinuous solutions
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
