Uniqueness Implies Existence and Uniqueness Conditions for a Class of (k + j)-Point Boundary Value Problems for n-th Order Differential Equations

摘要

For the n-th order nonlinear differential equation, y~((n)) = f(x, y,y',..., y~((n-1)), we consider uniqueness implies uniqueness and existence results for solutions satisfying certain (k + j)-point boundary conditions for 1 = j = n - 1 and 1 = k = n - j. We define (k; j)-point unique solvability in analogy to k-point disconjugacy and we show that (n - j_0; j_0)-point unique solvability implies (k; j)-point unique solvability for 1 = j = jo, and 1 = k = n - j. This result is analogous to n-point disconjugacy implies fc-point disconjugacy for 2 = k = n - 1.