Differential and Integral Equations

Existence of a periodic solution for implicit nonlinear equations

Veli-Matti Hokkanen

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The solvability of the periodic problem $$ v'(t)+\mathcal{B}(t)u(t)+\mathcal {C}(t)u(t)\ni \tilde f(t), \ \ v(t)\in A(t)u(t),\ \, v(0)=v(T), $$ will be investigated. It will be shown that the solution exists if $\mathcal {B}t)$ are maximal monotone operators, $\mathcal {A}(t)$ are subdifferentials, compact and possibly degenerated, $\mathcal {C}(t)$ are Lipschitzian and compact, and $\mathcal{B}(t)+\mathcal {C}(t)$ are coercive. The proof consists of several limit processes for an approximating periodic problem which has a solution.

Article information

Differential Integral Equations, Volume 9, Number 4 (1996), 745-760.

First available in Project Euclid: 7 May 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G10: Linear equations [See also 47D06, 47D09]
Secondary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions


Hokkanen, Veli-Matti. Existence of a periodic solution for implicit nonlinear equations. Differential Integral Equations 9 (1996), no. 4, 745--760. https://projecteuclid.org/euclid.die/1367969885

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