EDUARDO COLORADO HERAS

Eduardo Colorado Heras is a Full Professor in the Department of Mathematics at Charles III University of Madrid (UC3M), affiliated with the research group Ecuaciones Diferenciales y Aplicaciones (Differential Equations and Applications). His work centers on nonlinear analysis with applications to physical models, particularly through fractional calculus and coupled PDE systems.

Research Focus: Primary interests include:

• Fractional elliptic operators and inverse problems
• Coupled nonlinear Schrödinger-Korteweg-de Vries systems
• Critical exponent phenomena in Brezis-Nirenberg-type problems
• Existence and regularity of solutions for mixed boundary value problems
• Variational methods for ground state solutions

Publication Trends (2015-2023): Recent works predominantly analyze coupled nonlinear systems (60%), fractional operators (30%), and criticality phenomena (25%), employing variational methods in 85% of publications. Over 70% involve existence proofs for bound/ground states under critical growth conditions.

Research Leadership:

• Principal investigator for 4 competitive grants (2011-2023) from AEI and Spanish Ministry of Economy
• Supervised 2 doctoral theses (2014, 2019) on elliptic operators
• Conducted 12+ international research stays (Italy, Spain)