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Bifurcation of periodic solutions to differential inequalities in $$\mathbb{R}^ 3$$. (English) Zbl 0794.34031
The authors consider the inequality $$(*)$$ $$U(t)\in K$$, $$\forall t\in [0,T)$$, $$(\dot U(t)- A_ \lambda U(t)- G(\lambda,U(t)),\;v-U(t))\geq 0$$ for all $$v\in K$$, a.a. $$t\in [0,T)$$, where $$K$$ is a closed convex cone with its vertex at the origin in $$\mathbb{R}^ 3$$, $$A_ \lambda$$ is a real $$3\times 3$$ matrix depending continuously on a real parameter $$\lambda$$, $$G:\mathbb{R}\times\mathbb{R}^ 3\to\mathbb{R}^ 3$$ is a continuous mapping locally Lipschitzian in the variable $$u$$ and satisfying the usual condition $$\lim_{u\to 0} {G(\lambda,u)\over | u|}=0$$ uniformly on compact $$\lambda$$-intervals. Under certain assumptions concerning the eigenvalues of $$A_ \lambda$$ and a relation of the cone $$K$$ to the eigenvectors of $$A_ \lambda$$ they prove the existence of a bifurcation point $$\lambda_ I$$ at which periodic solutions to the inequality $$(*)$$ bifurcate from the branch of trivial solutions.
Reviewer: A.Martynyuk (Kiev)

##### MSC:
 34C23 Bifurcation theory for ordinary differential equations 34A40 Differential inequalities involving functions of a single real variable
##### Keywords:
bifurcation point; periodic solutions; inequality
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##### References:
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