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EXISTENCE AND UNIQUENESS OF WEAK AND CLASSICAL SOLUTIONS FOR A FOURTH-ORDER SEMILINEAR BOUNDARY VALUE PROBLEM

Part of: Elliptic equations and systems Thin bodies, structures

Published online by Cambridge University Press:  19 August 2019

CRISTIAN-PAUL DANET Open the ORCID record for CRISTIAN-PAUL DANET [Opens in a new window]
CRISTIAN-PAUL DANET*
Affiliation:
Department of Applied Mathematics, University of Craiova, Al. I. Cuza St., 13, 200585 Craiova, Romania email cristiandanet@yahoo.com
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Abstract

This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles.

Keywords

fourth-ordermaximum principleplate theoryPaneitz–Branson operator

MSC classification

Primary: 35J40: Boundary value problems for higher-order elliptic equations
Secondary: 35J35: Variational methods for higher-order elliptic equations 74K20: Plates
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 3 , July 2019 , pp. 305 - 319
Copyright
© 2019 Australian Mathematical Society 

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