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On the existence of anti-periodic solutions for implicit differential equations. (English) Zbl 1249.35001
The authors consider an implicit nonlinear evolution equation $\frac{d}{dt}(Bu)+Au+Gu=f$ in a Hilbert space $V$, where $B,A,G$ are operators from $V$ to its dual space $V'$, and $B$ is supposed to be a linear bounded symmetric and positive operator while $A+G$ is some perturbation of a monotone operator $A$. The following antiperiodic problem $Bu(0)=-Bu(T)$ is studied. Using the theory of pseudomonotone perturbations of maximal monotone mappings, the authors establish the existence of solutions of this problem.
Reviewer: Evgeniy Yu. Panov (Veliky Novgorod)

35A01Existence problems for PDE: global existence, local existence, non-existence
35A23Inequalities involving derivatives etc. (PDE)
47E05Ordinary differential operators
47J35Nonlinear evolution equations
Full Text: DOI
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