A link between global solvability and solvability over compacts for systems like : $(P(D_x, D_y) u = f, \ Qu = 0)$

Giuliano Bratti

Displaying similar documents to “A link between global solvability and solvability over compacts for systems like : $(P (D_{x}, D_{y}) u = f, Q u = 0)$ ”

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Consider boundary value problems for a functional differential equation $\{\begin{matrix} x^{(n)} (t) = (T^{+} x) (t) - (T^{-} x) (t) + f (t), & t \in [a, b], \\ l x = c, \end{matrix}$ where $T^{+}, T^{-} : 𝐂 [a, b] \to 𝐋 [a, b]$ are positive linear operators; $l : {𝐀𝐂}^{n - 1} [a, b] \to ℝ^{n}$ is a linear bounded vector-functional, $f \in 𝐋 [a, b]$ , $c \in ℝ^{n}$ , $n \geq 2$ . Let the solvability set be the set of all points $(𝒯^{+}, 𝒯^{-}) \in ℝ_{2}^{+}$ such that for all operators $T^{+}$ , $T^{-}$ with $∥ T^{\pm} ∥_{𝐂 \to 𝐋} = 𝒯^{\pm}$ the problems have a unique solution for every $f$ and $c$ . A method of finding the solvability sets are proposed. Some new properties of these sets are obtained in various cases. We continue the investigations of the solvability sets started...

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We investigate the solvability in continuous functions of the Abel equation φ(Fx) - φ(x) = 1 where F is a given continuous mapping of a topological space X. This property depends on the dynamics generated by F. The solvability of all linear equations P(x)ψ(Fx) + Q(x)ψ(x) = γ(x) follows from solvability of the Abel equation in case F is a homeomorphism. If F is noninvertible but X is locally compact then such a total solvability is determined by the same property of the cohomological...

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Displaying similar documents to “A link between global solvability and solvability over compacts for systems like : ( P ( D x , D y ) u = f , Q u = 0 ) ”

Displaying similar documents to “A link between global solvability and solvability over compacts for systems like : $(P (D_{x}, D_{y}) u = f, Q u = 0)$ ”