Nonlinear multivalued boundary value problems

Ralf Bader; Nikolaos S. Papageorgiou

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2001)

  • Volume: 21, Issue: 1, page 127-148
  • ISSN: 1509-9407

Abstract

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In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when d o m A ≠ ℝ N and d o m A = ℝ N , with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.

How to cite

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Ralf Bader, and Nikolaos S. Papageorgiou. "Nonlinear multivalued boundary value problems." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 21.1 (2001): 127-148. <http://eudml.org/doc/271491>.

@article{RalfBader2001,
abstract = {In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when $domA ≠ ℝ^\{N\}$ and $domA = ℝ^\{N\}$, with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.},
author = {Ralf Bader, Nikolaos S. Papageorgiou},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {usc and lsc multifunction; measurable selection; Leray-Schauder alternative theorem; Sobolev space; compact embedding; maximal monotone map; coercive map; surjective map; convex and nonconvex problem; nonlinear boundary conditions; differential inclusions},
language = {eng},
number = {1},
pages = {127-148},
title = {Nonlinear multivalued boundary value problems},
url = {http://eudml.org/doc/271491},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Ralf Bader
AU - Nikolaos S. Papageorgiou
TI - Nonlinear multivalued boundary value problems
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2001
VL - 21
IS - 1
SP - 127
EP - 148
AB - In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when $domA ≠ ℝ^{N}$ and $domA = ℝ^{N}$, with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.
LA - eng
KW - usc and lsc multifunction; measurable selection; Leray-Schauder alternative theorem; Sobolev space; compact embedding; maximal monotone map; coercive map; surjective map; convex and nonconvex problem; nonlinear boundary conditions; differential inclusions
UR - http://eudml.org/doc/271491
ER -

References

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  2. [2] R. Bader and N.S. Papageorgiou, Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions, Annales Polonici Math. LXIII (2000), 69-93. Zbl0991.34013
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  11. [11] N. Halidias and N.S. Papageorgiou, Existence and relaxation results for nonlinear second order multivalued boundary value problems in ℝ N , J. Diff. Eqns 147 (1998), 123-154. Zbl0912.34020
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  13. [13] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis. Volume I: Theory, Kluwer, Dordrecht, The Netherlands 1997. Zbl0887.47001
  14. [14] D. Kandilakis and N.S. Papageorgiou, Existence theorems for nonlinear boundary value problems for second order differential inclusions, J. Diff. Eqns 132 (1996), 107-125. Zbl0859.34011
  15. [15] R. Manasevich and J. Mawhin, Periodic solutions for nonlinear systems with p-Laplacian-like operators, J. Diff. Eqns 145 (1998), 367-393. Zbl0910.34051
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