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

Marek Izydorek, and Krzysztof P. Rybakowski. "Multiple solutions of indefinite elliptic systems via a Galerkin-type Conley index theory." Fundamenta Mathematicae 176.3 (2003): 233-249. <http://eudml.org/doc/286324>.

@article{MarekIzydorek2003,
abstract = {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.},
author = {Marek Izydorek, Krzysztof P. Rybakowski},
journal = {Fundamenta Mathematicae},
keywords = {equivariant Conley index; renormalized Morse index; Angenent–van der Vorst conjecture},
language = {eng},
number = {3},
pages = {233-249},
title = {Multiple solutions of indefinite elliptic systems via a Galerkin-type Conley index theory},
url = {http://eudml.org/doc/286324},
volume = {176},
year = {2003},
}

TY - JOUR
AU - Marek Izydorek
AU - Krzysztof P. Rybakowski
TI - Multiple solutions of indefinite elliptic systems via a Galerkin-type Conley index theory
JO - Fundamenta Mathematicae
PY - 2003
VL - 176
IS - 3
SP - 233
EP - 249
AB - 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.
LA - eng
KW - equivariant Conley index; renormalized Morse index; Angenent–van der Vorst conjecture
UR - http://eudml.org/doc/286324
ER -