Events

Pavel Drabek

University of West Bohemia, Czech Republic
Barton Lectures in Computational Mathematics
http://www.kma.zcu.cz/main.php?DRC=./STRUCTURE/02_pracovnici/&DRL=EN&DROF=0&nick=PaDra&KMAfile=./CLENOVE/main.php&kam=

When

Date: Tuesday, March 20, 2012 - Friday, March 23, 2012
Time: 4:00 pm
Location: Petty 150

Lecture 1: Monday, March 19, 2012, Petty 150, 4:00pm Reception: Lounge Petty 120, 3:30-4:00pm

We present some a priori estimates for the p-Laplacian-like equations and illustrate the difference between the semilinear (p=2) and quasilinear (1<p<2, p>2) case. We also relate the bifurcation result from the principal eigenvalue of the p- Laplacian and the Fredholm alternative-type result for nonlinear homogeneous operators. We illustrate the striking difference between the linear and nonlinear case.

Lecture 2: Tuesday, March 20, 2012, Petty 150, 4:00pm Reception: Lounge Petty 120, 3:30-4:00pm

We present the basic idea of the Nash-Moser iteration technique in order to prove the L^{\infty}- boundedness of the weak solution of a quasilinear boundary value problem. We prove the bifurcation from the first eigenvalue of the p-Laplacian, relate it to the bifurcation from infinity and the linearization of the p-Laplacian about the principal eigenfunction.

Lecture 3: Friday, March 23, 2012, Petty 150, 4:00pm Reception: Lounge Petty 120, 3:30-4:00pm

We discuss the existence and multiplicity results connected with the Fredholm alternative for the p-Laplacian at the first eigenvalue. We relate the bifurcation result to the variational structure of the problem. We also combine the variational approach with the method of lower and upper solutions to show how the lack of Palais-Smale condition can be overcome and prove the existence of a critical point.