Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 53, pp. 1-17.

Title: Uniqueness theorem for $p$-biharmonic equations

Author: Jiri Benedikt (Univ. of West Bohemia, Czech Republic)
         
Abstract: 
  The goal of this paper is to prove existence and uniqueness
  of a solution of the initial value problem for the equation
  $$
  (|u''|^{p-2}u'')''=\lambda |u|^{q-2}u
  $$
  where $\lambda\in{\mathbb{R}}$ and $p,q>1$.
  We prove the existence for $p\geq q$ only, and give a
  counterexample which shows that for $p<q$ there need not exist
  a global solution (blow-up of the solution can occur).
  On the other hand, we prove the uniqueness for $p\leq q$,
  and show that for $p>q$ the uniqueness does not hold true
  (we give a corresponding counterexample again).
  Moreover, we deal with continuous dependence of the solution on
  the initial conditions and parameters.
   
  
Submitted April 15, 2002. Published June 10, 2002.
Math Subject Classifications: 34A12, 34C11, 34L30.
Key Words: p-biharmonic operator; existence and uniqueness of solution;
     continuous dependence on initial conditions; jumping nonlinearity.