David Costa

David Costa is a Full Professor in the Department of Mathematical Sciences at the University of Nevada, Las Vegas (UNLV), where he has been a faculty member since 1993. His research is centered on partial differential equations and variational methods, particularly elliptic type equations modeling steady-state phenomena. He is affiliated with the Center for Applied Math & Statistics at UNLV.

• Ph.D. in Mathematics, Brown University (1973)
• B.S. in Electrical Engineering, Universidade Federal de Pernambuco, Brazil (1967)

David Costa's research focuses on the theoretical and applied aspects of nonlinear partial differential equations. He employs variational and topological methods from nonlinear analysis to study existence, multiplicity, and qualitative properties of solutions. His work often involves critical nonlinearities, semipositone problems, Hamiltonian systems, and inequalities in Sobolev spaces. He has made significant contributions to the understanding of logistic-type equations, Kirchhoff problems, and Schrodinger-type models.

The recent publications highlight a strong trend in critical and subcritical elliptic problems in unbounded domains, particularly in R^N and exterior domains. His work frequently explores variational characterizations, Nehari manifolds, and maximum principles. Many papers involve collaborations with H. Tehrani, J. do O’, and others, focusing on symmetry, concentration phenomena, and nonstandard growth conditions.

Notable scientific contributions include foundational work on Caffarelli-Kohn-Nirenberg inequalities, Hardy-Rellich inequalities, and Trudinger-Moser type embeddings. While no formal awards are listed, his sustained publication record in top journals and editorial contributions reflect high scholarly recognition.

Costa has advised several students and collaborators, though specific names are not listed in the provided text. He has contributed to research grants and collaborative projects, particularly in nonlinear analysis and PDEs. His work on mathematical biology, including a forthcoming book, indicates interdisciplinary outreach. He has also held leadership roles in the Brazilian Mathematical Society and the CNPq advisory committee.

David Costa is associated with the Center for Applied Math & Statistics at UNLV, where he participates in research seminars and collaborative programs. His work environment supports theoretical and applied mathematical research, especially in differential equations and variational methods.