2006 International Conference: Electron. J. Diff. Eqns. Electronic Journal of Differential Equations: Conference 21, 2014.

Proceedings of the Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems. Northern Arizona University - Flagstaff, Arizona, USA. June 6t-9, 2012.


This conference is a continuation of two very successful conferences. Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms that was organized by J.M. Neuberger in Flagstaff in June 2002, where open questions and numerical algorithms for variational methods were the dominant theme and Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems organized by M. Chhetri, P. Girg, J.M. Neuberger (Conference chair) and N. Sieben with expanded focus and agenda. The 2012 conference closely resembles the structure and focus established in 2007.

The organizing committee consisted of the following members: John M. Neuberger (conference chair; Northern Arizona University, Flagstaff AZ, USA), Maya Chhetri (University of North Carolina at Greensboro, Greensboro NC, USA), Petr Girg (University of West Bohemia, Pilsen, Czech Republic) and Peter Takac (University of Rostock, Germany).

The scientific committee consisted of the following members: Alfonso Castro (Harvey Mudd College, Claremont CA, USA), Goong Chen (Texas A&M University, College Station TX, USA), Pavel Drabek (University of West Bohemia, Pilsen, Czech Republic), Tim Kelley (North Carolina State University, Raleigh NC, USA), and Ratnasingham Shivaji (University of North Carolina at Greensboro, Greensboro NC,, USA).

The conference was aimed at researchers, graduate students, and advanced undergraduate students working in various areas of Nonlinear Analysis, Differential Equations, and their applications. Five leading experts in their respective fields Monica Clapp (Mexico), Pavel Drabek (Czech Republic), Jean-Michel Rakotoson (France), Peter Takac (Germany), Jacques Giacomoni (France) each gave at least two one-hour keynote presentations. Some of the plenary talks were aimed at introducing topics from variational/topological methods to graduate students and junior researchers. There were 55 contributed 30-minute talks. Plenty of time was allotted for small group discussions and informal interaction among beginning researchers and experts in the field.

This conference proceedings comprise only of a small subset of talks presented at the conference. This volume contains 15 mathematical papers; one article authored by a keynote speaker. As the title of our conference suggests, most of the topics concerns variational and/or topological methods as applied to nonlinear elliptic PDE. There was a focus on open problems; hence papers with conjectures were encouraged. Survey papers were also solicited, as were works featuring applications.

This conference successfully brought together those doing cutting-edge nonlinear functional analysis with researchers more computationally oriented; hence some of the papers in this volume feature numerical investigations. It was our intent to survey what is known in the general subject area, list the important open questions, and suggest analytical and numerical techniques that might be beneficial to those seeking to make progress towards solving those open problems. We hope that the reader will find this volume an excellent starting point for considering new problems and relevant techniques in nonlinear elliptic and related PDE.

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