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 $pq$ 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.