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

We examine the equation \\Delta^2 u = \lambda fu \qquad \Omega, \ with either Navier or Dirichlet boundary conditions. We show some uniqueness results under certain constraints on the parameter $\lambda$. We obtain similar results for the sytem {equation*} \{{array}{rrl} -\Delta u &=& \lambda fv \qquad \Omega -\Delta v &=& \gamma gu \qquad \Omega, u&=& v = 0 \qquad \partial Omega. {array}. {equation*}

Author: Craig Cowan

Source: https://archive.org/