Multiple solutions of indefinite elliptic systems via a Galerkin-type Conley index theory

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

Abstrakty

EN

Let Ω be a bounded domain in $ℝ^{N}$ with smooth boundary. Consider the following elliptic system:
$-Δu = ∂_{v}H(u,v,x)$ in Ω,
$-Δv = ∂_{u}H(u,v,x)$ in Ω,
u = 0, v = 0 in ∂Ω. (ES)
We assume that H is an even "-"-type Hamiltonian function whose first order partial derivatives satisfy appropriate growth conditions. We show that if (0,0) is a hyperbolic solution of (ES), then (ES) has at least 2|μ| nontrivial solutions, where μ = μ(0,0) is the renormalized Morse index of (0,0). This proves a conjecture by Angenent and van der Vorst.

Kategorie tematyczne

• 58E50: Applications
• 58E40: Group actions
• 35J50: Variational methods for elliptic systems
• 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel\cprime man) theory, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 176
• Numer: 3
• Strony: 233-249

Daty

wydano

2003

Twórcy

autor

Marek Izydorek

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

autor

Krzysztof P. Rybakowski

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

Identyfikatory

DOI

10.4064/fm176-3-3