Uniqueness theorem for p-biharmonic equations

Electronic Journal of Differential Equations

关键词: p-biharmonic operator;    existence and uniqueness of solution;    continuous dependence on initial conditions;    jumping nonlinearity.;   

DOI  :  

来源: DOAJ

【 摘 要 】

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 $pq$ 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.

【 授权许可】

Unknown