Uniqueness Theorem for p-biharmonic Equations

Date

2002-06-10

Authors

Benedikt, Jiri

Journal Title

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Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

The goal of this paper is to prove existence and uniqueness of a solution of the initial value problem for the equation (|u''|p-2u'')'' = 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.

Description

Keywords

p-biharmonic operator, Existence and uniqueness of solution, Continuous dependence on initial conditions, Jumping nonlinearity

Citation

Benedikt, J. (2002). Uniqueness theorem for $p$-biharmonic equations. <i>Electronic Journal of Differential Equations, 2002</i>(53), pp. 1-17j.

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Attribution 4.0 International

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