Some Remarks on Some Second-Order Elliptic Differential Equations

Details Some Remarks on Some Second-Order Elliptic Differential Equations Some Remarks on Some Second-Order Elliptic Differential Equations

2003-08-14

arxiv.org/abs/math/0308137v1

Mathematics

Classical Analysis and ODEs

9 pages, first report

Scientific paper

We are concerned with the almost automorphic solutions to the second-order elliptic differential equations of type $\ddot u(s) + 2 B \dot u(s) + A u(s) = f(s) (\ast),$ where $A, B$ are densely defined closed linear operators acting in a Hilbert space ${\mathbb H}$ and $f: {\mathbb R} \mapsto {\mathbb H}$ is a vector-valued almost automorphic function. Using invariant subspaces, it will be shown that under appropriate assumptions; every solution to $(\ast)$ is almost automorphic.

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