Abstract
Sufficient conditions of solvability and unique solvability of the boundary value problem
u
(m)(t) = f(t, u(τ
11(t)), . . . , u(τ
1k
(t)), . . . , u
(m–1)(τ
m1(t)), . . .
. . . , u
(m–1)(τ
mk
(t))), u(t) = 0, for t ∉ [a, b],
u
(i–1)(a) = 0 (i = 1, . . . , m – 1), u
(m–1)(b) = 0,
are established, where τ
ij
: [a, b] → R (i = 1, . . . , m; j = 1, . . . , k) are measurable functions and the vector function f : ]a, b[×Rkmn
→ Rn
is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.
GENERALIZATION OF RIEMANN-HILBERT BOUNDARY VALUE PROBLEM FOR A FIRST ORDER NONLINEAR COMPLEX PARTIAL DIFFERENTIAL EQUATION