Uniqueness Theorem for p-biharmonic Equations
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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")" = λ|u| q-2 u where λ ∈ ℝ and p, q > 1. We prove the existence for p ≥ 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 ≤ 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.
CitationBenedikt, J. (2002). Uniqueness theorem for $p$-biharmonic equations. Electronic Journal of Differential Equations, 2002(53), pp. 1-17j.
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