We consider a boundary value problem (0.1) -y′ (x) + q(x)y(x) = f(x), x ∈ R, lim|x|→∞ y(x) = 0, where f(x) ∈ Lp(R), p ∈ [1, ∞] (L∞(R) := C(R)) and 0 ≤ q(x) ∈ L1loc(R). Boundary value problem (0.1) is called correctly solvable in the given space Lp(R) if for any f(x) ∈ Lp(R) there is a unique solution y(x) ∈ Lp(R) and the following inequality ∥y∥p ≤ c(P) ∥f∥p, for all f(x) ∈ Lp(R), holds with absolute constant c(p) ∈ (0, ∞). We find criteria for correct solvability of the problem (0.1) in Lp(R).
|Number of pages||14|
|State||Published - 24 Sep 2002|
- Correct solvability
- First order linear differential equation
ASJC Scopus subject areas
- Mathematics (all)