Uniqueness of solutions for elliptic systems and fourth order equations involving a parameter

2011/09/23 by Cowan, Craig
#35Jxx #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.5206

Abstract

We examine the equation Δ² u = λf(u) Ω, with either Navier or Dirichlet boundary conditions. We show some uniqueness results under certain constraints on the parameter λ. We obtain similar results for the sytem equation* \arrayrrl -Δu &=& λf(v) Ω, -Δv &=& γg(u) Ω, u&=& v = 0 ∂ Omega. array. equation*

Related

• Uniqueness results for higher order elliptic equations and systems
• Uniqueness results for semilinear elliptic systems on \Rⁿ
• Uniqueness of solutions for an elliptic equation modeling MEMS
• A uniqueness result for some singular semilinear elliptic equations
• Quantitative uniqueness of solutions to second order elliptic equations with singular lower order terms