Differential and Integral Equations

Strongly nonlinear multivalued, periodic problems with maximal monotone terms

Evgenia H. Papageorgiou and Nikolaos S. Papageorgiou

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

Export citation