## Anti-periodic solutions to a class of nonlinear differential equations in Hilbert space.(English)Zbl 0743.34067

The boundary value problem $$-au''(t)+bu'(t)+\partial\varphi(u(t))- \partial\psi(u(t))\ni f(t)$$, a.e. $$f\in R$$, $$u(t+T)=-u(t)$$, in a real Hilbert space $$H$$ is considered. Here $$a\geq 0$$, $$b\neq 0$$, $$T>0$$, $$f\in L^ 2_{loc}(R;H)$$ satisfies $$f(t+T)=-f(t)$$ a.e. $$t\in R$$, $$\varphi$$ and $$\psi$$ are convex, even functionals on $$H$$ and “$$\partial$$” stands for subdifferential. The existence of solution of this problem is studied by the methods of the theory of multi-valued monotone operators. The applications of the achieved results to nonlinear partial differential equations are discussed.

### MSC:

 34G20 Nonlinear differential equations in abstract spaces 34C25 Periodic solutions to ordinary differential equations
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### References:

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