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

Advisor of 15 PhD Thesis, author of 210 research papers and 10 books,  editor of another 6, among them, the Proceedings of the 10th AIMS Conference, the largest congress on Differential Equations and Dynamical Systems  ever held with over 2300 participants, he has served as member of the editorial boards of:

• Advanced Nonlinear Studies
• Nonlinear Analysis
• Rendiconti dell'Istituto di Matematica dell'Universtà di Trieste (RIMUT)
• Abstract and Applied Analysis
• Journal of Applied Mathematics
• Applied Mathematics
• Mathematics

Moreover, he has been Guest Professor and taught advanced courses in the Mathematical Institute of the Zürich University, the University of Trieste, the National Center for Theoretical Sciences (NCTS) of Taiwan, the Tsing Hua University at Hsinchu (Taiwan), the Xi'an Jiao-Tong University (China), the Ferhat Abbas University (Algeria), the National Institute for the Development of the Chemical Industry at Santa Fe (Argentina), as well as in the Universities of Buenos Aires and Bahía Blanca (Argentina), and the Andes at Mérida (Venezuela). He has given scientific tours through Argentina (Santa Fe, Córdoba, Buenos Aires, Rosario, San Juan, Bahía Blanca, Rosario and La Plata, South Korea (Seoul, Pohang and Pusan) and Taiwan (Taipei, Hsinchu and Kaohsiung), and has delivered seminars, among other places,  at Moscow, Kyoto, Hiroshima, Kitakyushu, Fukuoka, Beijing, Xi’an, Tianjin, Taiyuan, Banff, Toronto, Winnipeg, Halifax, Manhattan KA, Madison WI, San Antonio TX, Miami FL, Orlando FL, Dallas TX, Irvine CAL, Sydney (Australia), and the Courant Institute of Mathematical Sciences of the New York University, where he  was very honored of discussing mathematics with the Abel recipients L. Nirenberg, in February 1997, and S. R. S. Varadhan, in July 2014.

He has collaborated intensively with extremely influential mathematicians, as H. Amann, E. N. Dancer, and P. H. Rabinowitz, former President of the Section of Mathematics of the Academy of Sciences of the United States, who, together with F. Zanolin and P. Omari, integrates the Research Team of his Research Grant PID2021-123343NB-I00.

 

Research interests

His main research interests cover nonlinear Partial Differential Equations and Reaction-Diffusion  systems, continuous Dynamical Systems, Spatial Ecology and Population Dynamics, Spectral Theory of linear operators, Topological Degree and abstract Nonlinear Analysis, as well as Numerical Analysis and Fluid Dynamics.

Complete CV of his Research Group at:

 https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=115790

 

Latest Publications

• 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

• S. Cano-Casanova, S. Fernández-Rincón, J. López-Gómez. A singular perturbation result for a class of periodic-parabolic BVPs. Open Mathematics, 22 (1). 2024. DOI: 10.1515/math-2024-0020.
• J. López-Gómez, P. H. Rabinowitz, F. Zanolin. Non-negative solutions of a sublinear elliptic problem. Journal of Fixed Point Theory and Applications, 26. 2024. DOI: 10.1007/s11784-024-01120-z.
• P. Cubillos, J. López-Gómez, A. Tellini. High multiplicity of positive solutions in a superlinear problem of Moore–Nehari type. Communications in Nonlinear Science and Numerical Simulation, 136. 2024. DOI: 10.1016/j.cnsns.2024.108118.
• J. López-Gómez, V.K. Ramos, C.A. Santos, A. Suárez. Point-wise behavior of the explosive positive solutions to a degenerate elliptic BVP with an indefinite weight function. Journal of Differential Equations, 403, 67–86. 2024. DOI: 10.1016/j.jde.2024.05.006.
• J. López-Gómez, E. Muñoz-Hernández. Minimal complexity and chaos in periodic predator-prey models. Rendiconti del Seminario Matematico di Torino, 81 (1), 133 – 158. 2023. Link: http://www.seminariomatematico.polito.it/rendiconti/81-1.html.
• 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. López-Gómez, P. Omari. Regular versus singular solutions in quasilinear indefinite problems with sublinear potentials. Journal of Differential Equations, 372, 2023. pp. 1-54. https://doi.org/10.1016/j.jde.2023.06.034
• J. López-Gómez, E. Muñoz-Hernández, F. Zanolin. Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments. Open Mathematics. 2023, 21 (1), 1-54. Special Issue on Future Directions of Further Developments in Mathematics. https://doi.org/10.1515/math-2022-0593
• J. López-Gómez, 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
• J. López-Gómez, E. Muñoz-Hernández. Large saturation effects provoke multiplicity in spatially heterogeneous predator-prey models. Proceedings of the XXVII Congreso de Ecuaciones Diferenciales y Aplicaciones / XVII Congreso de Matemática Aplicada, Prensas de la Universidad de Zaragoza, 2023. https://www.doi.org/10.26754/uz.978-84-18321-66-5
• J. López Gómez, E. Muñoz Hernández, F. Zanolin. Rich dynamics in planar systems with heterogeneous nonnegative weights. Communications on Pure and Applied Analysis. 2023. volumen 22, 1043-1098.https://www.aimsciences.org/article/doi/10.3934/cpaa.2023020
• 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. López-Gómez, P. Omari. Optimal regularity results for the one-dimensional prescribed curvature equation via the strong maximum principle. Journal of Mathematical Analysis and Applications, 2023, 512(2). https://doi.org/10.1016/j.jmaa.2022.126719
• 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. 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
  
• 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-Gómez, E. 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-Gómez. Solution 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, 33, 1. 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-Gómez, P. 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-Gómez. Solution 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. 33, 1. 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

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