Boundary data smoothness for solutions of nonlocal boundary value problems for \(n\)-th order differential equations. (English) Zbl 1151.34016

Henderson, Johnny; Hopkins, Britney; Kim, Eugenie; Lyons, Jeffrey

Involve 1, No. 2, 167-181 (2008).

Summary: Under certain conditions, solutions of the boundary value problem, \[ y(n)=f(x,y,y^{\prime},\dots,y^{(n-1)}), \]
\[ y^{(i-1)}(x_1)=y_i \quad\text{ for }1\leq i\leq n-1,\text{ and }y(x_2)-\sum_{i=1}^m r_iy(\eta_i)=y_n, \]
are differentiated with respect to boundary conditions, where \(a<x_1<\eta_1<\cdots<\eta_m<x_2<b\), and \(r_1,\dots,r_m,y_ 1,\dots,y_n\in\mathbb R\).

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations
34B08	Parameter dependent boundary value problems for ordinary differential equations

Keywords:

nonlinear boundary value problem; ordinary differential equation; nonlocal boundary condition; boundary data smoothness