Institutos Universitarios

Julián López-Gómez

Catedrático de Universidad (Full Professor)
Department of Applied Mathematics and Mathematical Analysis
School of Chemical Sciences
Complutense University of Madrid
Nonlinear Elliptic and Parabolic Equations UCM-GR17-970846

 

 

 

Bio

Author of 190 papers and 10 books, he has delivered advanced courses at the MI of Zürich, the NCTS of Taiwan, the TU of Xian (China), the Universities of Buenos Aires, Bahía Blanca, Santa Fe (Argentina), Mérida (Venezuela) and Trieste (Italy), has given scientific tours through Argentina, South Korea and Taiwan, and has given seminars at the Courant Institute of NYU, the MI of the UW-Madison, the MI of the UTSA, the MI of Kyoto and Hiroshima, the MI of the University of Sydney, the Fields Institute of Toronto, and the POSTECH of South Korea. According to the files of the MSN of the AMS he has got 2553 citations by 741 authors with ih=28, though, according to GS, his ih equals 37. He is the main researcher of the Excellence Group UCM-GR17-970846.

 

Research interests

His main research interests cover nonlinear PDEs and RD systems, spatial ecology and population dynamics, spectral theory of linear operators, topological degree and abstract nonlinear analysis, as well as continuous dynamical systems, numerical analysis, and fluid dynamics.

 

Latest Publications

  • M. Fencl, J. López-Gómez. Global bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problems. Nonlinearity. 2022, 35, 3, 1213 - 1248. https://doi.org/10.1088/1361-6544/ac4a88
  • P. Cubillos, J. Lopez-Gomez, A. Tellini. Multiplicity of nodal solutions in classical non-degenerate logistic equations. Electronic Research Archive. 2022, 30, 3, 898-928. https://doi.org/10.3934/era.2022047
  • J. López-Gómez, P. Omari. Branches of positive solutions of a superlinear indefinite problem driven by the one-dimensional curvature operator. Applied Mathematics Letters. 2022, 126, 107807. https://doi.org/10.1016/j.aml.2021.107807
  • J. López-Gómez, J. C. SampedroAxiomatization 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
  • W. T. Li, J. López-Gómez, J. W. Sun. Sharp Blow-Up Profiles of Positive Solutions for a Class of Semilinear Elliptic Problems. Advanced Nonlinear Studies. 2021, 21, 4, 751-765. https://doi.org/10.1515/ans-2021-2149
  • W. T. Li, J. López-Gómez, J. W. Sun. Sharp Blow-Up Profiles of Positive Solutions for a Class of Semilinear Elliptic Problems. Advanced Nonlinear Studies. 2021. https://doi.org/10.1515/ans-2021-2149
  • J. López-GómezE. Muñoz-Hernández, F. Zanolin. Minimal complexity of subharmonics in a class of planar periodic predator-prey models. Proceedings of the XXVI Congreso de Ecuaciones Diferenciales y Aplicaciones. XVI Congreso de Matemática Aplicada. 2021, 258–264. ISBN: 978-84-18482-21-2 https://digibuo.uniovi.es/dspace/handle/10651/59093
  • J. López-Gómez, E. Muñoz-Hernández, F. Zanolin. The Poincaré-Birkhoff Theorem for a Class of Degenerate Planar Hamiltonian Systems. Advanced Nonlinear Studies. 2021, 21, 3, 489 – 499. https://doi.org/10.1515/ans-2021-2137
  • 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
  • W. T. Li, J. López-Gómez, J. W. Sun. Sharp patterns of positive solutions for some weighted semilinear elliptic problems. Calculus of Variations and Partial Differential Equations. 2021, 60, Article number 85. https://doi.org/10.1007/s00526-021-01993-9
  • S. Fernández-Rincón, J. López-Gómez. The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics. Nonlinear Analysis: Real World Applications. 2021, 60, Article number 103285. https://doi.org/10.1016/j.nonrwa.2020.103285
  • M. Fencl, J. López- Gómez. Nodal solutions of weighted indefinite problems. Journal of Evolution Equations. 2020. https://doi.org/10.1007/s00028-020-00625-7
  • 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
  • J. López-Gómez, P. Omari. Regular Versus Singular Solutions in a Quasilinear Indefinite Problem with an Asymptotically Linear Potential. Adv. Nonlinear Stud. 2020, 20(3), 557–578. https://doi.org/10.1515/ans-2020-2083
  • J. López-Gómez, E. Muñoz-Hernández. A spatially heterogeneous predator-prey model. Discrete and Continuous Dynamical Systems Series B. 2020. https://www.aimsciences.org/article/doi/10.3934/dcdsb.2020081 
  • D. Aleja, I. Antón, J. López-Gómez, Global structure of the periodic positive solutions for a general class of periodic-parabolic logistic equations with indefinite weights. Journal of Mathematical Analysis and Applications, 2020; 487, 1, 123961. https://doi.org/10.1016/j.jmaa.2020.123961
  • D. Aleja, I. Antón, J. López-GómezSolution components in a degenerate weighted BVP. Nonlinear Analysis, Theory, Methods and Applications. 2020, 192, 111690. https://doi.org/10.1016/j.na.2019.111690 
  • J. López-Gómez. Protection Zones in Periodic-Parabolic Problems. Advanced Nonlinear Studies. 2020, 20, 2. https://doi.org/10.1515/ans-2020-2084
  • J. López-Gómez, E. Muñoz-Hernández. Global structure of subharmonics in a class of periodic predator-prey models. Nonlinearity. 2020, 331. DOI: https://doi.org/10.1088/1361-6544/ab49e1
  • J. López-Gómez, E. Muñoz-Hernández, F. Zanolin. On the applicability of the Poincaré–Birkhoff twist theorem to a class of planar periodic predator-prey models. Discrete and Continuous Dynamical Systems Series A. 40(4): 2020, 2393-2419. https://www.aimsciences.org/article/doi/10.3934/dcds.2020119 
  • J. López-Gómez, P. Omari. Characterizing the formation of singularities in a superlinear indefinite problem related to the mean curvature operator. Journal of Differential Equations. 2020, 269, 2, 1544-1570. https://www.sciencedirect.com/science/article/pii/S0022039620300218
  • J. López-GómezP. H. Rabinowitz. The structure of the set of 1-node solutions of a class of degenerate BVP’s. J. Differential Equations. 2020, 268, 8, 4691-4732. https://doi.org/10.1016/j.jde.2019.10.040
  • J. López-Gómez, P. H. Rabinowitz. The structure of the set of 1-node solutions of a class of degenerate BVP’s. J. Differential Equations, 2019, https://doi.org/10.1016/j.jde.2019.10.040
  • D. Aleja, I. Antón, J. López-GómezSolution components in a degenerate weighted BVP. Nonlinear Analysis. 192, March 2020, 111690. https://doi.org/10.1016/j.na.2019.111690 
  • J. López-Gómez, E. Muñoz-Hernández. Global structure of subharmonics in a class of periodic predator-prey models. Nonlinearity. 331. DOI: https://doi.org/10.1088/1361-6544/ab49e1
  • I. Antón, J. López-Gómez. Principal eigenvalue and maximum principle for cooperative periodic-parabolic systems. Nonlinear Anal. 178 (2019), 152–189.  https://doi.org/10.1016/j.na.2018.07.014
  • S. Fernández-Rincón, J. López-Gómez. The Singular Perturbation Problem for a Class of Generalized Logistic Equations under Non-classical Mixed Boundary Conditions (2019) Advanced Nonlinear Studies, 19 (1), pp. 1-27. DOI: https://doi.org/10.1515/ans-2018-2034
  • J. López-Gómez, L. Maire. Uniqueness of large solutions for non-monotone nonlinearities. Nonlinear Anal. Real World Appl. 47 (2019)291–305. https://doi.org/10.1016/j.nonrwa.2018.11.003
  • J. López-Gómez, P. Omari. Global Components of Positive Bounded Variation Solutions of a One-Dimensional Indefinite Quasilinear Neumann Problem (2019) Advanced Nonlinear Studies, 19 (3), pp. 437-473 DOI: https://doi.org/10.1515/ans-2019-2048

Contact details

julian@mat.ucm.es

 

Metasolutions of Parabolic Equations in Population Dynamics, CRC Press, Boca Raton, 2015

 

Linear Second Order Elliptic Operators, World Publishing, Singapore, 2013