Research
My  research interests  include:
(1) Existence and bifurction of solutions to semilinear and quasilinear boundary value
problems for nonlinear ordinary and partial differential systems.
(2) Topological methods in nonlinear analysis and differential equations, especially degree theories and Conley index.
(3) Mathematical biology.

 

Professional Experience

Pan American University, Edinburgh, Texas: Assistant Professor, 1976-79

University of Alabama, Tuscaloosa, Alabama:

Assistant Professor, 1979-81

Associate Professor, 1981-85

Professor, 1985-89

University of Alabama at Birmingham:

Professor, 1989-

Université Catholique de Louvain, Belgium; May 1983

SISSA, Trieste, Italy;  May and June, 1984

University of Granada, Spain;  September, 1990

Université Catholique de Louvain, Belgium;  April and May, 1996

University of Chile, August 2002

University of Turin, Italy, September 2003

University of Chile, October and November, 2003

Université Catholique de Louvain, Belgium; September 2004

Doctoral Students:

Wan Se Kim, "Boundary Value Problems for Non-Linear Telegraph Equations in One Space Dimension," 1987.

Yong-Hoon Lee, "Ambrosetti-Prodi Type Results for Periodic Solutions of Second Order Ordinary Differential Systems," 1990.

Sarah Al-Sheik,  "A Study of Bifurcation for Non-Autonomous Orinary Differential Equations," 1996.

Doctoral Committes:

Chi-Tsung Huang, “Approximate Modeling and Time-Optimal Control of a Disstillation Column,”   Chemical Engineering, University of Alabama-Tuscaloosa, 1981

Anton Von Backhaus, “A Generalization of Hermite Polynomials,” Mathematics, University of Alabama- Tuscaloosa,  1983

William T. Logan, “Computation of Transport Coefficients by Molecular Dynamics Simulation,” Physics, University of Alabama-Tuscaloosa, 1988

Joo Ho Kang, “On the Unicellularity of Certain Operators,” Mathematics, University of Alabama- Tuscaloosa, 1988.

David Arcoya Alvarez,  “Existencia y Multiplicidad de Soluciones para Problemas de Contorno Ellipticos  Seminales en Resonancia,” Universidad de Granada, Spain, 1990

David E. England, “A Mathematical Analysis of Nocturnal Slope Flows”  Applied Mathematics, University of  Alabama at Huntsville, 1993

Xiaojing Zhang, “On Linear and Nonlinear Stability Theory of Periodic Flows of Incompressible Fluid,”  Applied Mathematics, University of Alabama-Tuscaloosa, 1995

Joyce Kam-Ping Yung, “Mathematical Applications of Diffusion Equations in Cancer Tumor Growth,”  Applied Mathematics, University of Alabama at Birmingham, 1997

Aureliano M. Robles Pérez, “Las Soluciones Periódicas de una Ecuación de la Cuerda Vibrante con Disipación,”  Mathemática Aplicada, Universidad de Granada, Spain, 2000.

Thomas Park, "Age Structure in Epidemic Models of Vector-Borne Infections," 2004, University of Alabama-Huntsville

Dawn Duehring, current UAH applied mathematics student.

Selected Professional Service 

Refereed for NSF and other American and foreign funding agencies, and many journals, including: Journal of Differential  Equations, Journal of Mathematical Analysis and Applications, Discrete and Continuous Dynamical Systems, Transactions of the American Mathematical Society,  Proceedings of the American Mathematical Society,  Nonlinear Analysis,  London Mathematical Society, and Communications in Partial Differential Equations.

Organizer (with Raul Manasevich) of a Special Session on Quasilinear Partial Differential Equations, International Conference on Dynamical Systems and Differential Equations, Wilmington, NC, May 2002.

Organizer (with Wenzhang Huang) of a Special Session on Nonlinear Partial Differential Equations and Applications,  AMS meeting, Birmingham, Alabama,  November 10-12,  2000.

Organizer (with Gilbert Weinstein) of a Special Session on Nonlinear Partial Differential Equations, AMS meeting, Chatanooga, Tennessee, October 11-12, 1996.

Co-Director,  UAB International Conference on Differential Equations and Mathematical Physics, Birmingham, March, 1990.

Member, Organizing Committee, UAB/UA International Conference on Differential Equations and Mathematical Physics, held March 1986 at UAB.

Department Faculty Affairs Committee, 1997-2000.

UAB Mathematics Graduate Program Director,  1996-1997

Mathematics Graduate Committee, 1992-97

UAB School of Science and Mathematics Faculty Affairs Committee,  1991-93,  1995-97

Fast-Track masters degree program committee, 1993-96.

Joint Program Committee for the PhD in Applied Mathematics, 1989-91, 1996-97

Graduate Director, Mathematics, UA, Tuscaloosa, 1984-85, 1988-89

College of Arts and Sciences Tenure and Promotion Committee, UA, 1985-87.

Selected invited lectures

Special session on Monotonicity Methods in Differential equations (A. G. Kartsatos, organizer), American Mathematical Society, Denver,  January, 1983.

Conference on Topological Methods in Boundary Value Problems for Ordinary  Differential Equations, SISSA, Trieste, Italy, May, 1984.

Seminar talk, University of Florence, Italy, June 1984.

Lecture, Universite de Louvain, Louvain-la-Neuve, Belgium, March, 1985.

Oberwolfach conference on ordinary differential equations, Germany, March, 1985.

First United States-Chile International Conference on Nonlinear Analysis and Differential Equations, Santiago, Chile, April, 1985.

Memphis State University, May, 1985: Three lectures on critical point theory and applications to differential equations.

Conference on Nonlinear Partial Differential Equations, University of Utah, February, 1986.

Colloquium, University of South Florida, November, 1986.

Colloquium, Auburn University, February, 1987.

Oberwolfach conference on ordinary differential equations, Germany, March 1987.

Special Session on Nonlinear Functional Analysis (P. J. Milojevic, organizer), American Mathematical Society,  Newark, New Jersey, April 1987.

Memphis State University, May, 1987.

Mississippi State University, February, 1988.

International Conference on Differential equations, Columbus, Ohio, March 1988.

Universite de Louvain, Louvain-la-Neuve, Belgium, March 1989.

University of Houston, April, 1989.

Lecture, Universite de Louvain, Louvain-la-Neuve, Belgium, October 1990.

Lecture, Georgia Institute of Technology, January 1991.

Special Session on Nonlinear Boundary Value Problems (R. K. Nagle, organizer), American Mathematical  Society, Tampa, Florida,  March, 1991.

Emory University "Dixieland Analysis Seminar," April 1991.

University of North Texas, March 1992.

International Conference on Differential Equations and Mathematical Physics, Georgia Institute of Technology, March 1992.

World Congress of Nonlinear Analysts, Tampa Florida, August 1992. Special sessions on Periodic Solutions of Boundary Value Problems and on Topological
   and Variational Methods in Nonlinear Boundary Value Problems.

University of Tennessee, Knoxville, Tenn., December, 1992.

Special Session on Reaction-Diffusion Equations (W. E. Fitzgibbon and Jeff Morgan, organizers), American Mathematical Society, Texas A&M, College Station, Texas, October, 1993. 

IMACS Conference, Atlanta, Georgia, Special Session on Reaction-  Diffusion Equations (W. E. Fitzgibbon, organizer), July, 1994.

Special Session on Boundary Value Problems (P. J. McKenna and A. C. Lazer, organizers), American Mathematical Society,  Hartford, Conn., March 3-4, 1995.

Oberwolfach conference on ordinary differential equations, Oberwolfach, Germany, March 19-24, 1995; lecture on Conley index  and bifurcation.

Georgia Institute of Technology, lecture "Global bifurcation in  dynamical systems," May 2, 1995.

Fourth International Conference on Population dynamics, Rice University,  Houston, Texas, May 23-27, 1995; Special Session on Systems of Partial
    Differential  Equations in  Biology (W. Fitzgibbon, organizer), lecture ``Global bifurcation in reaction-  diffusion systems.''

Annual Meeting on Differential Equations, U. de Louvain-Free University, Brussels,  March 1, 1996,  lecture, "Conley index and bifurcation."

"Conley index and bifurcation.," Departemento de Mathemática Aplicada, Unversity of Granada, Spain, April 9, 1996, lecture,

Special Session on Critical Point Theory (Daniela Lupo, organizer), International Conference on Differential  Equations  in honor of the 60th birthday of Alan C. Lazer, University of Miami, Florida, January,  1999.

International Conference on Differential Equations and Related Topics, Pusan National University, Pusan, South Korea, June 1-3, 1999,
Lecture, "Bounded Solutions of Differential Equations."

Colloquium lecture,  'Bounded Solutions of Differential Equations,"  Hanyang University, Seoul, Korea, June 4, 1999.

Special Session on Variational and Topological Methods (A. Fonda, organizer), International Conference on Dynamical Systems  and Differential Equations, Kennesaw, Georgia,  May 18--21, 2000.

Lecture, Departemento de Mathemática Aplicada, Universidad de Granada, Granada, Spain, September, 2000.

Special Session on Nonlinear Boundary Value Problems (Anna Capietto, organizer), Conference on Dynamical Systems and Differential Equations, Wilmington, NC, May 2002.

"Intoduction to degree theory and bifurcation," Joint Program Meeting,Birmingham, Alabama, Fall 2002.

Colloquium Talk, Auburn University, November 22, 2002.

“Bifurcation at Resonance”,  University of Turin, September, 2003.

“Conley index and bifurcation,” Center for Mathematical Modeling, University of Chile, Nov. 10, 2004.

“Bifurcation and existence results for systems of differential equations,” World Conference of Nonlinear Analysts July 2004, Orlando, Florida. Special Session organized by G. Hetzer and W. Shen.

“Global bifurcation in systems of differential equations,”  lectures given at Université  Catholique de Louvain, Belgium, October 2004.

“Rotation numbers and global bifurcation in systems,” Departamento de Análisis Matemático , Universidad de Granada, Granada, Spain, November 2004.

“Global bifurcation in systems of differential equations,” Colloquium talk, University of Alabama at Huntsville, Nov. 12, 2004.

"Bifurcation from infinity in systems of ordinary differential equations," Special  Session in Honor of Klaus Schmitt, organized by Steve Cantrell and Chris Cosner.in  the Sixth MSU-UAB Conference on Differential Equations & Computational Simulations, Starkville, Mississippi, May 13-14, 2005.