Structure of the solution set for a partial differential inclusion

Yi Cheng; Ravi P. Agarwal; Afif Ben Amar; Donal O’Regan

doi:10.1186/s13662-015-0723-0

Structure of the solution set for a partial differential inclusion

Yi Cheng, Ravi P. Agarwal, Afif Ben Amar, Donal O’Regan

Mathematics

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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 Rδ$R_{\delta}$ 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.

Original language	English
Article number	380
Pages (from-to)	1-18
Number of pages	18
Journal	Advances in Difference Equations
Volume	2015
Issue number	1
DOIs	https://doi.org/10.1186/s13662-015-0723-0
Publication status	Published - 1 Dec 2015

Keywords

biharmonic problem
compact δ
differential inclusion
path-connected
set-valued mapping

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Cheng, Yi and Agarwal, Ravi P. and Ben Amar, Afif and O'Regan, Donal

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10.1186/s13662-015-0723-0

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title = "Structure of the solution set for a partial differential inclusion",

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 Rδ\$R\_\{\textbackslash{}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.",

keywords = "biharmonic problem, compact δ, differential inclusion, path-connected, set-valued mapping",

author = "Yi Cheng and Agarwal, \{Ravi P.\} and \{Ben Amar\}, Afif and Donal O{\textquoteright}Regan",

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T1 - Structure of the solution set for a partial differential inclusion

AU - Cheng, Yi

AU - Agarwal, Ravi P.

AU - Ben Amar, Afif

AU - O’Regan, Donal

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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 Rδ$R_{\delta}$ 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.

AB - 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 Rδ$R_{\delta}$ 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.

KW - biharmonic problem

KW - compact δ

KW - differential inclusion

KW - path-connected

KW - set-valued mapping

UR - https://www.scopus.com/pages/publications/84950324251

U2 - 10.1186/s13662-015-0723-0

DO - 10.1186/s13662-015-0723-0

M3 - Article

SN - 1687-1839

VL - 2015

SP - 1

EP - 18

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 380

ER -

Structure of the solution set for a partial differential inclusion

Abstract

Keywords

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