# 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

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topRalf 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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