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2004 Strongly nonlinear multivalued, periodic problems with maximal monotone terms
Evgenia H. Papageorgiou, Nikolaos S. Papageorgiou
Differential Integral Equations 17(3-4): 443-480 (2004).


In this paper we study periodic, nonlinear, second-order differential inclusions, driven by the differential operator $$ x\rightarrow (\alpha(x)\|x'\|^{p-2}x')' $$ and involving a maximal monotone term $A$ and a multivalued nonlinearity $F(t,x)$ which satisfies the Hartman condition. We do not assume that $domA$ is all of $\mathbb{R}^{N}$, and so our formulation incorporates variational inequalities. Then we obtain partial generalizations. First, we allow $F$ to depend on $x'$, but for $p=2$ and for the scalar problem ($N=1$). Second, we assume a general multivalued, nonlinear differential operator $x\rightarrow \alpha(x,x')'$; the nonlinearity $F$ depends also on $x'$, but the boundary conditions are Dirichlet. Our methods are based on notions and techniques from multivalued analysis and from the theory of operators of monotone type.


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Evgenia H. Papageorgiou. Nikolaos S. Papageorgiou. "Strongly nonlinear multivalued, periodic problems with maximal monotone terms." Differential Integral Equations 17 (3-4) 443 - 480, 2004.


Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1224.34024
MathSciNet: MR2037985

Primary: 34G25
Secondary: 34A60 , 34B15

Rights: Copyright © 2004 Khayyam Publishing, Inc.


Vol.17 • No. 3-4 • 2004
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