In this paper we consider the following Toda system of equations on a compact surface: −Δu₁ = 2ρ1 (h₁eᵘ1 ⁻ ¹) − ρ2 (h₂eᵘ² ⁻ ¹) , −Δu₂ = 2ρ2 (h₂eᵘ² ⁻ ¹) − ρ1 (h₁eᵘ1 ⁻ ¹) . Here h₁, h₂ are smooth positive functions and ρ1, ρ2 two positive parameters. In this note we compute the Leray-Schauder degree mod ℤ₂ of the problem for ρᵢ ∈ (4πk, 4π(k + 1)) (k ∈ ℕ). Our main tool is a theorem of Krasnoselskii and Zabreiko on the degree of maps symmetric with respect to a subspace. This result yields new existence results as well as a new proof of previous results in the literature."

On the Leray-Schauder degree of the Toda system on compact surfaces

MALCHIODI, ANDREA
;
2015

Abstract

In this paper we consider the following Toda system of equations on a compact surface: −Δu₁ = 2ρ1 (h₁eᵘ1 ⁻ ¹) − ρ2 (h₂eᵘ² ⁻ ¹) , −Δu₂ = 2ρ2 (h₂eᵘ² ⁻ ¹) − ρ1 (h₁eᵘ1 ⁻ ¹) . Here h₁, h₂ are smooth positive functions and ρ1, ρ2 two positive parameters. In this note we compute the Leray-Schauder degree mod ℤ₂ of the problem for ρᵢ ∈ (4πk, 4π(k + 1)) (k ∈ ℕ). Our main tool is a theorem of Krasnoselskii and Zabreiko on the degree of maps symmetric with respect to a subspace. This result yields new existence results as well as a new proof of previous results in the literature."
2015
Settore MAT/05 - Analisi Matematica
Geometric PDEs; Leray-schauder degree;
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/60617
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