Lecture: WOJCIECH KRYSZEWSKI, 15:00-16:00, 30, August, Nicolaus Copernicus University



Abstract We study the Schr?dinger   equations u+ V (x)u = f(x; u) in and

u-λu = f(x; u)in a bounded domain. We assume that f is superlinear but

of subcritical growth and is nondecreasing. In we also assume that V and f are periodic in . We show that these equations have a ground state and that there exist infinitely many solutions if f is odd in u. The results generalize those od Szulkin and Weth, where was assumed to be strictly increasing. This seemingly small change forces us to go beyond methods of smooth analysis. The work is joint with F. de Paiva and A. Szulkin.

Introduction: Prof. Wojciech Kryszewski is   a professor of Nicolaus Copernicus University, Poland, and a managing editor   of the journal: Topological Methods in Nonlinear Analysis published by the   Schauder Center for Nonlinear Studies. He is also a director of the Schauder   Center for Nonlinear Studies. His main research interests are functional   analysis, nonlinear analysis, semigroup theory, nonlinear partial   differential equations, and so on. He has published about 60 papers in the   journals such as: Trans. Amer. Math. Soc.Topol. Methods Nonlinear   Anal.SIAM J. Control Optim.Proc. Amer.Math. Soc..


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