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

Canadian mathematical bulletin

Johnny Henderson²  Rahmat Ali Khan¹  Paul W. Eloe³ 

[1] Centre for Advanced Mathematics and Physics, National University of Sciences and Technology(NUST), Campus of College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan;Department of Mathematics, Baylor University, Waco, TX, 76798-7328, USA;Department of Mathematics, University of Dayton, Dayton, OH, 45469-2316, USA

关键词: boundary value problem;    uniqueness;    existence;    unique solvability;    nonlinear interpolation;   

DOI  :  10.4153/CMB-2011-117-0

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

For the $n$-th order nonlinear differential equation, $y^{(n)} = f(x, y, y',dots, y^{(n-1)})$, we consider uniqueness implies uniqueness and existenceresults for solutions satisfying certain $(k+j)$-pointboundary conditions for $1le j le n-1$ and $1leq k leq n-j$. Wedefine $(k;j)$-point unique solvability in analogy to $k$-pointdisconjugacy and we show that $(n-j_{0};j_{0})$-pointunique solvability implies $(k;j)$-point unique solvability for $1le j lej_{0}$, and $1leq k leq n-j$. This result is analogous to$n$-point disconjugacy implies $k$-point disconjugacy for $2le klen-1$.

【 授权许可】

Unknown