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