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  4. Juan Carlos Sampedro Pascual

Juan Carlos Sampedro Pascual

Associate Professor
Department of Applied Mathematics to Industrial Engineering
School of Engineering and Industrial Design
Universidad Politécnica de Madrid
Nonlinear Elliptic and Parabolic Equations UCM-GR17-970846

 

 

Research interests

My research is focused on advancing our comprehension of analysis and topology within infinite-dimensional spaces, and exploring how this knowledge manifests across diverse mathematical disciplines. These include vector bundle theory, partial differential equations (PDEs), and quantum field theory. 

Although my study is split into two seemingly distinct fields, they share significant intersections that enrich the overall research.

Nonlinear Functional Analysis: 

  • Topological Degree Theory 

  • Bifurcation Theory on Banach spaces

  • Nonlinear Spectral Theory and Applications to topological K-Theory

  • Nonlinear Elliptic & Parabolic Partial Differential Equations

Real and Harmonic Analysis:

  • Measures on Infinite Dimensional Spaces

  • Projective Limits of Probability Measures

  • Wiener Measure on Riemannian Manifolds

  • Path Integrals and Constructive Quantum Field Theory

 

Latest Publications

  • J. C. Sampedro. Periodic solutions to nonlocal pseudo-differential equations. A bifurcation theoretical perspective. Nonlinear Analysis, 254. 2025. DOI: 10.1016/j.na.2025.113746.
  • J. López-Gómez and J. C. Sampedro. Blow-up estimates and a priori bounds for the positive solutions of a class of superlinear indefinite elliptic problems. Nonlinear Analysis, 251. 2025. DOI: 10.1016/j.na.2024.113693.
  • J. López-Gómez, J. C. Sampedro. Bifurcation Theory for Fredholm Operators. Journal of Differential Equations, 404, 182-250, 2024. DOI: 10.1016/j.jde.2024.05.040.
  • J. C. Sampedro. On the Lp-Spaces of Projective Limits of Probability Measures. Journal of Theoretical Probability, 37, 2665–2703. DOI: 10.1007/s10959-024-01329-1.
  • J. C. Sampedro. On the colimits of certain Sobolev spaces. Journal of Mathematical Analysis and Applications, 535 (2). 2024. DOI: 10.1016/j.jmaa.2024.128141.
  • J. C. Sampedro. Existence of Infinite Product Measures. Real Analysis Exchange, 48(2), 271-284, (2023). https://doi.org/10.14321/realanalexch.48.2.1643257005
  • López-Gómez and J. C. Sampedro, Orientability through the algebraic multiplicity. Journal of Fixed Point Theory Applications.2023, 25, Art. Number: 60. https://doi.org/10.1007/s11784-023-01062-y
  • G. Feltrin, J. C. Sampedro, F. Zanolin. Periodic solutions to superlinear indefinite planar systems: A topological degree approach. Journal of Differential Equations, 2023, 363, 5. https://doi.org/10.1016/j.jde.2023.03.042
  • J. L. Gómez, J. C. Sampedro. Generating loops and isolas in semilinear elliptic BVP's. Nonlinear Analysis, volumen 232, 2023, 113268, ISSN 0362-546X. https://doi.org/10.1016/j.na.2023.113268
  • J. C. Sampedro. Approximation Schemes for Path Integration on Riemannian Manifolds. Journal of Mathematical Analysis and Applications. 2022, 512, 2, Article number 126176. https://doi.org/10.1016/j.jmaa.2022.126176
  • J. López-Gómez, J. C. Sampedro. Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier. Journal of Fixed Point Theory and Applications. 2022, 24, 1, Article number 8. https://doi.org/10.1007/s11784-021-00916-7
  • J. López-Gómez, J. C. Sampedro. New analytical and geometrical aspects of the algebraic multiplicity. Journal of Mathematical Analysis and Applications. 2021, 504, 1, 125375. https://doi.org/10.1016/j.jmaa.2021.125375
  • J. López-Gómez, J. C. Sampedro. Global Perturbation of Nonlinear Eigenvalues. Advanced Nonlinear Studies. 2021, https://doi.org/10.1515/ans-2021-2127
  • J. López-Gómez, J. C. Sampedro. Algebraic multiplicity and topological degree for Fredholm operators. Nonlinear Analysis. 2020, 201, 112019. https://doi.org/10.1016/j.na.2020.112019