Research

My research interests are divided into two themes: 

Nonlinear Functional Analysis: 

Real and Harmonic Analysis:


Published Articles

Bifurcation Theory for Fredholm Operators.

Journal of Differential Equations, Volume 404, (2024). 

DOI: doi.org/10.1016/j.jde.2024.05.040 


On the L^p-spaces of Projective Limits of Probability Measures

Journal of Theoretical Probability, (2024).

DOI: doi.org/10.1007/s10959-024-01329-1 


On the colimits of certain Sobolev spaces,

Journal of Mathematical Analysis and Applications, Volume 535, Issue 2, (2024).

DOI: doi.org/10.1016/j.jmaa.2024.128141 

Existence of infinite product measures

Real Analysis Exchange, Volume 42, (2023).  

DOI: doi.org/10.14321/realanalexch.48.2.1643257005 

Orientability through the algebraic multiplicity

Journal of Fixed Point Theory and Applications, Volume 25, (2023). 

DOI: doi.org/10.1007/s11784-023-01062-y 

Periodic solutions to superlinear indefinite planar systems: a topological degree approach

Journal of Differential Equations, Volume 363, (2023). 

DOI: doi.org/10.1016/j.jde.2023.03.042 

Generating loops and isolas in semilinear elliptic BVP’s

Nonlinear Analysis, Volume 232, 113268 (2023). 

DOI: doi.org/10.1016/j.na.2023.113268 

Approximation schemes for path integration on Riemannian manifolds

Journal of Mathematical Analysis and Applications

Volume 512, Issue 2 (2022).  

DOI: doi.org/10.1016/j.jmaa.2022.126176 

Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier,   

Journal of Fixed Point Theory and Applications, Volume 24, Number 8 (2022).

DOI: doi.org/10.1007/s11784-021-00916-7 

New analytical and geometrical aspects of the algebraic multiplicity

Journal of Mathematical Analysis and Applications, Volume 504, Issue 1 (2021). 

DOI: doi.org/10.1016/j.jmaa.2021.125375 

Global perturbation of nonlinear eigenvalues

Advanced Nonlinear Studies, Volume 21, Issue 2 (2021), 229-249. 

DOI: doi.org/10.1515/ans-2021-2127 

Algebraic multiplicity and topological degree for Fredholm operators,

Nonlinear Analysis, Volume 201, 112019 (2020). 

DOI: doi.org/10.1016/j.na.2020.112019 

On the space of infinite dimensional integrable functions

Journal of Mathematical Analysis and Applications, Volume 488, Issue 1 (2020). 

DOI: doi.org/10.1016/j.jmaa.2020.124043 

Some identities involving Inverse Gamma integrals

The Ramanujan Journal, Volume 48, (2019), 577–583. 

DOI: doi.org/10.1007/s11139-018-0082-z 

On a new constant related to Euler’s constant

The Ramanujan Journal, Volume 46, (2018), 77–89. 

DOI: doi.org/10.1007/s11139-017-9912-7 

Some unit square integrals

The Ramanujan Journal, Volume 40, (2016), 541–555. 

DOI: doi.org/10.1007/s11139-016-9787-z 

Submitted Papers

Periodic solutions to nonlocal pseudo-differential equations. A bifurcation theoretical perspective, Submitted. 

ArXiv: arxiv.org/abs/2409.04253v1 

Blow-up estimates and a priori bounds for the positive solutions of a class of superlinear indefinite elliptic problems, Submitted. 

ArXiv: arxiv.org/abs/2402.01519

Research Stays

Research Stay at Università degli Studi di Palermo.

Under the supervision of Professor Francesca Dalbono. (Palermo, Italy)

Research Stay at BCAM (Basque Center for Applied Mathematics).

Under the supervision of Professor Luis Vega. (Bilbao, Spain)

Invited Stay at Swansea University (Prifysgol Abertawe).

Under the supervision of Professor Elaine Crooks. (Swansea, United Kingdom)

Invited Stay at Dipartimento di Scienze Matematiche, Politecnico Turin.

Under the supervision of Professor Jacobo Pejsachowicz. (Turin, Italy)

Research Stay at Dipartimento di Scienze Matematiche, Informatiche e Fisiche of the Universit‘a degli Studi di Udine.

Under the supervision of Professors Fabio Zanolin and Guglielmo Feltrin. (Udine, Italy)


Research Projects

Project PID2021-123343NB-I00: Ecuaciones Diferenciales Heterogéneas: Dinámica y Numérico

PI: Julián López-Gómez, 

Ministerio de Ciencia, innovación y universidades, Gobierno de España.

Project PGC2018-097104-B-I00: Sistemas de Reacción Difusión

PI: Julián López- Gómez, 

Ministerio de Ciencia, innovación y universidades, Gobierno de España.


Research Institutions & Groups


Research Group: Análisis Matemático y Aplicaciones (A.M.A)

PI: Dolores Barrios Rolanía

Universidad Politécnica de Madrid (UPM).

Research Group: Linear and Non-Linear Waves (WAVE) — Analysis of partial differential equations (APDE)

PI: Luis Vega, 

Basque Center for Applied Mathematics (BCAM).

Instituto de Matemática Interdisciplinar (IMI)

Universidad Complutense de Madrid (UCM). 

Research group UCM-GR17-970846: Nonlinear Elliptic and Parabolic Equations

PI: Julián López-Gómez, 

Universidad Complutense de Madrid (UCM).


Fellowships and Awards

Agencia Nacional de Evaluación de la Calidad y Acreditación (ANECA).

Ministerio de Ciencia e Innovación, Gobierno de España.

Expedient Code: JDC2022-048469-I

2nd position in the area of Mathematics.

Agencia Nacional de Evaluación de la Calidad y Acreditación (ANECA).

Gobierno Vasco

Grant for predoctoral stays. 

Expedient Code: EP_2022_1_0063.

Grants for the attendance of young researchers to the ICM2022.

Gobierno Vasco.

Expedient Code: PRE_2019_1_0220. 

The unique grant in the field Mathematics.

Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid (UCM).

Gobierno Vasco

Director: Luis Escauriaza Zubiria. 

Expedient Code: IkasC_2017_1_0191

Gobierno Vasco

Third position in Science.