Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory

Smaïl Djebali; Abdelghani Ouahab

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2010)

  • Volume: 30, Issue: 1, page 23-49
  • ISSN: 1509-9407

Abstract

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In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are provided.

How to cite

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Smaïl Djebali, and Abdelghani Ouahab. "Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 30.1 (2010): 23-49. <http://eudml.org/doc/271135>.

@article{SmaïlDjebali2010,
abstract = {In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are provided.},
author = {Smaïl Djebali, Abdelghani Ouahab},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {differential inclusions; boundary value problem; fixed point; compact; convex; nonconvex; decomposable; continuous selection; controllability},
language = {eng},
number = {1},
pages = {23-49},
title = {Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory},
url = {http://eudml.org/doc/271135},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Smaïl Djebali
AU - Abdelghani Ouahab
TI - Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2010
VL - 30
IS - 1
SP - 23
EP - 49
AB - In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are provided.
LA - eng
KW - differential inclusions; boundary value problem; fixed point; compact; convex; nonconvex; decomposable; continuous selection; controllability
UR - http://eudml.org/doc/271135
ER -

References

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