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Uniqueness theorem for p-biharmonic equations

BENEDIKT, J. Uniqueness theorem for p-biharmonic equations. Electronic Journal of Differential Equations, 2002, roč. 2002, č. 53, s. 1-17. ISSN: 1072-6691
Jazyk publikace: eng
Anglický název: Uniqueness theorem for p-biharmonic equations
Rok vydání: 2002
Autoři: Jiří Benedikt
Abstrakt EN: 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 $\lamda\in\mathbb{R}$ 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.
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