Uniqueness theorem for p-biharmonic equations
Jiřı́ Benedikt · DOAJ (DOAJ: Directory of Open Access Journals) · 2002
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 $p q$ 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.