Florin Catrina

Teaching:
Graduate Courses: Probability I and II, Mathematical Modeling, Applied Analysis, History of Mathematics, Modern Geometries

Undergraduate Courses: University Calculus (I, II, III, IV), Topics in Mathematics, Math for Liberal Arts, Statistics for Pharmacy, Applied Probability for Actuarial Sciences, Precalculus, Calculus for Business, Calculus with Biological

Applications, Mathematical Theory of Probability and Statistics

Research:
Applied Analysis: nonlinear analysis, weighted Sobolev spaces, continuous/compact embeddings, integral/differential inequalities, isoperimetric inequalities

Partial Differential Equations: elliptic PDE’s, existence and qualitative properties of solutions, applications, nonlinear partial differences equations, spectral analysis

22. Diagonals of Green’s Functions and Applications, Nonlinear Anal. 119 (2015), 398-418, (with Z.-Q. Wang).

21. Nonexistence of positive radial solutions for a problem with singular potential, Adv. Nonlinear Anal. 3 (2014), no. 1, 1-13.

20. Traveling wave solutions for a chemotaxis system, BIOMAT 2013, 43-62, World Sci. Publ., Hackensack, NJ, 2014, (with V. Reyes).

19. On the mean value property of harmonic functions on graphs, Indian J. Math. 53 (2011), suppl., 107-114, (with J. Colanduoni).

18. A Note on solutions concentrating on spheres, Indian J. Math. 52 (2010), suppl., 11-20.

17. A refinement of the radial Pohozaev identity, Mathematica Bohemica, 135 (2010) 143-150 Proceedings of the Equadiff12 Conference, Brno, Czech Republic.

16. Radial Solutions for critical elliptic equations in three and four dimensions, Indian Journal of Mathematics, Vol. 51 (2009), 31-37.

15. A note on a result of M. Grossi, Proceedings of the American Mathematical Society, 137 (2009), no. 11, 3717-3724.

14. Sharp weighted-norm inequalities for functions with compact support in R^N \ {0}, Journal of Differential Equations, 246 (2009), no. 1, 164-182, (with D. Costa).

13. Compact embeddings for a class of weighted Hilbert spaces, Indian Journal of Mathematics, Golden Jubilee Year Volume, (2008) 61-70.

12. Positive solutions for nonlinear elliptic equations with fast increasing weights, Proceedings of the Royal Society of Edinburgh: Section A 137A (2007) 1157-1178, (with M. Furtado and M. Montenegro).

11. On a Brezis-Nirenberg type problem, Electronic Journal of Differential Equations 2006, No. 146, 10 pp. (electronic).

10. Nonexistence of bounded energy solutions for a critical exponent problem, Journal of Differential Equations 215 19-36 (2005).

9. Critical nonlinearities and symmetric solutions, ”Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms”, Contemporary Mathematics 357 239-249 (2004).

8. Radial solutions for weighted semilinear equations, Communications in Contemporary Mathematics 4 529-545 (2002), (with R. Lavine).

7. Asymptotic uniqueness and exact symmetry of k-bump solutions for a class of degenerate elliptic problems, Proceedings of the Third International Conference on Dynamical Systems and Differential Equations 80-87 (2001), (with Z.-Q. Wang).

6. A one-dimensional nonlinear degenerate elliptic equation, Proceedings of the USA-Chile Workshop on Nonlinear Analysis, Conf. 6 89-99 (2001), (with Z.-Q. Wang).

5. Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in R^N, Ann. Inst. Henri Poincar´e, Analyse Non Lin`eaire 18 157-178 (2001), (with Z.-Q. Wang).

4. On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence) and symmetry of extremal functions, Communications in Pure and Applied Mathematics 54 229-258 (2001), (with Z.-Q. Wang).

3. Symmetric solutions for the prescribed scalar curvature problem, Indiana University Mathematics Journal 49 779-813 (2000), (with Z.-Q. Wang).

2. On the Caffarelli-Kohn-Nirenberg inequalities, C. R. Acad. Sci. Paris 330 437442 (2000), (with Z.-Q. Wang).

1. Nonlinear elliptic equations on expanding symmetric domains, Journal of Differential Equations 156 153-181 (1999), (with Z.-Q. Wang).

Teaching Publications

1. WeBWorK: Online Homework Delivery System, Professional Studies Review 4 No 2 29-34 (2009).