Uniqueness theorem for p-biharmonic equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F02%3A00070409" target="_blank" >RIV/49777513:23520/02:00070409 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Uniqueness theorem for p-biharmonic equations
Original language description
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 $lamdainmathbb{R}$ and $p,q>1$. We prove the existence for $pgeq q$ only, and givea 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F00%2F0376" target="_blank" >GA201/00/0376: Non-linear boundary value problems-existence and multiplicity results bifurcations</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2002
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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