Uniqueness Theorem for p-biharmonic Equations
| dc.contributor.author | Benedikt, Jiri | |
| dc.date.accessioned | 2020-08-10T21:24:33Z | |
| dc.date.available | 2020-08-10T21:24:33Z | |
| dc.date.issued | 2002-06-10 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Benedikt, J. (2002). Uniqueness theorem for $p$-biharmonic equations. <i>Electronic Journal of Differential Equations, 2002</i>(53), pp. 1-17j. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12352 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | p-biharmonic operator | |
| dc.subject | Existence and uniqueness of solution | |
| dc.subject | Continuous dependence on initial conditions | |
| dc.subject | Jumping nonlinearity | |
| dc.title | Uniqueness Theorem for p-biharmonic Equations | |
| dc.type | Article |