On the Conley index in Hilbert spaces in the absence of uniqueness

• Autorzy: Marek Izydorek , Krzysztof P. Rybakowski
• Języki publikacji: EN

Abstrakty

EN

Consider the ordinary differential equation
(1) ẋ = Lx + K(x)
on an infinite-dimensional Hilbert space E, where L is a bounded linear operator on E which is assumed to be strongly indefinite and K: E → E is a completely continuous but not necessarily locally Lipschitzian map. Given any isolating neighborhood N relative to equation (1) we define a Conley-type index of N. This index is based on Galerkin approximation of equation (1) by finite-dimensional ODEs and extends to the non-Lipschitzian case the ℒ𝓢-Conley index theory introduced in [9]. This extended ℒ𝓢-Conley index allows applications to strongly indefinite variational problems ∇Φ(x) = 0 where Φ: E → ℝ is merely a C¹-function.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 171
• Numer: 1
• Strony: 31-52

Daty

wydano

2002

Twórcy

autor

Marek Izydorek

• Faculty of Technical Physics, and Applied Mathematics, Technical University Gdańsk, Narutowicza 11/12, 80-952 Gdańsk, Poland

autor

Krzysztof P. Rybakowski

• Fachbereich Mathematik, Universität Rostock, Universitätsplatz 1, 18055 Rostock, Germany

Identyfikatory

DOI

10.4064/fm171-1-2