Differential and Integral Equations

Strongly nonlinear multivalued, periodic problems with maximal monotone terms

Evgenia H. Papageorgiou and Nikolaos S. Papageorgiou

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Abstract

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

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

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060440

Mathematical Reviews number (MathSciNet)
MR2037985

Zentralblatt MATH identifier
1224.34024

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

Citation

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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