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Anti-periodic boundary value problems for higher order differential equations in Hilbert spaces. (English) Zbl 0779.34054

This paper extends the ideas of the second and third author [J. Funct. Anal. 99, 387-408 (1991; Zbl 0743.34067)] to higher order equations. More precisely, the authors investigate the existence of solutions of the boundary value problem \(\alpha_ n u^{(n)}(t)+Au(t)+\beta\partial\psi(u(t))\ni f(t)\), \(0<t<T\), \(u^{(k)}(0)=-u^{(k)}(T)\), \(k=0,\dots,n-1\), in a real Hilbert space \(H\), where \(A\) is linear self-adjoint monotone operator, \(\partial\psi\) denotes the subdifferential of a proper convex, lower semicontinuous function \(\psi: H\to(-\infty,+\infty]\), \(f\in L^ 2(0,T;H)\), \(\beta=\pm1\), \(n>2\) and \(\alpha_ n=1\) if \(n\) is odd and \(\alpha_ n=(- 1)^{n/2}\) if \(n\) is even. The results are based on the study of the existence, uniqueness and continuous dependence on \(f\) of solutions of the same problem with \(\beta=0\).

MSC:

34G20 Nonlinear differential equations in abstract spaces

Citations:

Zbl 0743.34067
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References:

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