Differential and Integral Equations

Strongly nonlinear multivalued, periodic problems with maximal monotone terms

Evgenia H. Papageorgiou and Nikolaos S. Papageorgiou

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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.

Article information

Differential Integral Equations Volume 17, Number 3-4 (2004), 443-480.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G25: Evolution inclusions
Secondary: 34A60: Differential inclusions [See also 49J21, 49K21] 34B15: Nonlinear boundary value problems


Papageorgiou, Evgenia H.; Papageorgiou, Nikolaos S. Strongly nonlinear multivalued, periodic problems with maximal monotone terms. Differential Integral Equations 17 (2004), no. 3-4, 443--480. https://projecteuclid.org/euclid.die/1356060440.

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