Article Contents
Article Contents

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

• We examine the equation $$\Delta^2 u = \lambda f(u) \qquad \Omega,$$ 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 \begin{eqnarray} &-\Delta u = \lambda f(v) \qquad \Omega, \\ &-\Delta v = \gamma g(u) \qquad \Omega, \\ &u= v = 0 \qquad \partial \Omega. \end{eqnarray}
Mathematics Subject Classification: 35J55, 35B05, 35K50, 35K55.

 Citation:

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