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Structure of the solution set for a partial differential inclusion

Cheng, Yi
; 
Agarwal, Ravi P
; 
Ben Amar, Afif
; 
O’Regan, Donal
Identifiers
http://hdl.handle.net/10379/10761
 https://doi.org/10.13025/25373
Publication Date
2015-12-01
Keywords
biharmonic problem, differential inclusion, set-valued mapping, path-connected, compact r-delta, boundary-value-problems, nonlinear evolution inclusions, weighted sobolev spaces, discontinuous nonlinearities, biharmonic problem, multivalued perturbations, topological-structure, decomposable values, periodic-solutions, frechet spaces
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Article
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Cheng, Yi; Agarwal, Ravi P; Ben Amar, Afif; O’Regan, Donal (2015). Structure of the solution set for a partial differential inclusion. Advances in Difference Equations ,
Abstract
In this paper, we consider the biharmonic problem of a partial differential inclusion with Dirichlet boundary conditions. We prove existence theorems for related partial differential inclusions with convex and nonconvex multivalued perturbations, and obtain an existence theorem on extremal solutions, and a strong relaxation theorem. Also we prove that the solution set is compact R-delta if the perturbation term of the related partial differential inclusion is convex, and its solution set is path-connected if the perturbation term is nonconvex.
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Springer Nature
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)