| Summary: | 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 $lambdain{mathbb{R}}$ and $p,q>1$. We prove the existence for $pgeq q$ 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 $pleq q$, 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.
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