Report 29/2005: Topological and variational methods for differential equations (June 26th -- July 2nd, 2005 (0526)) (Q870671)

Summary: These notes contain the extended abstracts of the talks presented at the workshop. The range of topics includes nonlinear Schrödinger equations, singularly perturbed equations, symmetry and nodal properties of solutions, long-time dynamics for parabolic equations, Morse theory. Contributions: {\parindent=6mm \begin{itemize}\item[--]Antonio Ambrosetti, Nonlinear Schrödinger Equations with Potentials Vanishing at Infinity (p. 1605) \item[--]Zhi-Qiang Wang, On Some Weighted Hardy-Sobolev Inequality (p. 1606) \item[--]Susanna Terracini, A variational problem for the spatial segregation of reaction-diffusion systems and related problems (p. 1609) \item[--]Nils Ackermann, Solution Set Splitting at Low Energy Levels in Nonlinear Schrödinger Equations with Periodic and Symmetric Potentials (p. 1613) \item[--]Wolfgang Reichel, Uniqueness theorems in the calculus of variations by the method of transformation groups (p. 1614) \item[--]Matthias Winter, Spikes for the Gierer-Meinhardt System -- Analysis and Numerical Simulation (p. 1617) \item[--]Andrea Malchiodi (joint with Zindine Djadli and Cergy Pontoise), Existence of Conformal Metrics with Constant Q-Curvature (p. 1621) \item[--]Nassif Ghoussoub, A class of self-dual partial differential equations and its variational principles (p. 1623) \item[--]Filomena Pacella, Sign Changing Solutions of Semilinear Elliptic Equations: Symmetry and Critical Exponent Problems (p. 1627) \item[--]Yihong Du, Boundary blow-up solutions with interior layers and spikes (p. 1628) \item[--]Claudia Wulff (joint with George W. Patrick and Mark Roberts), Stability of Poisson Equilibria (p. 1632) \item[--]Massimo Grossi, Asymptotic behaviour of the Kazdan-Warner solution in the annulus (p. 1634) \item[--]Juncheng Wei, On The Number of Interior Peak Solutions for a Singularly Perturbed Neumann Problem (p. 1636) \item[--]Robert C.A.M. Vandervorst (joint with R.W. Ghrist, J.B. van den Berg), Braids and parabolic dynamics (p. 1639) \item[--]Chang Shou Lin, Mean field equations and Green functions on torus (p. 1645) \item[--]Michel Willem, Nonlinear Elliptic Equations with Critical Hardy Potential (p. 1648) \item[--]Pavol Quittner, Liouville-type theorems for superlinear parabolic problems (p. 1649) \item[--]Pietro Majer (joint with Alberto Abbondandolo), The Morse complex for infinite dimensional manifolds (p. 1651) \item[--]Tobias Weth, Energy bounds for entire nodal solutions of autonomous elliptic equations via the moving plane method (p. 1652) \item[--]Jean van Schaftingen, Symmetrization and Symmetry of Critical Points (p. 1654) \item[--]Shusen Yan (joint with E.N.Dancer), Elliptic Problems of Ambrosetti-Prodi Type (p. 1657) \item[--]Abbas Bahri, Morse lemma at infinity for the sign-changing Yamabe problem (p. 1658) \item[--]Bernold Fiedler (joint with Hiroshi Matano), Brouwer Degree for Nodal Blow-up (p. 1661) \item[--]Patricio Felmer, Critical exponents for uniformly elliptic extremal operators (p. 1661) \item[--]Kazunaga Tanaka (joint with Yohei Sato), Sign-changing multi-bump solutions for NLS with steep potential wells (p. 1664) \item[--]Florin Catrina (joint with Richard Lavine), On the Brezis-Nirenberg Problem (p. 1667) \item[--]Yuan Lou, On the joint actions of diffusion and spatial heterogeneity on single and multiple species (p. 1670) \end{itemize}}