Solutions of 2\(n\)th Lidstone boundary value problems and dependence on higher order derivatives. (English) Zbl 1029.34019

The authors consider the Lidstone boundary value problem \[ \begin{gathered} (-1)^nu^{2n}(x)= f(x, u(x), u''(x),\dots, u^{2(n-1)}(x)),\quad 0< x< 1,\\ u^{(2i)}(0)= u^{(2i)}(1)= 0,\quad 0\leq i\leq n-1.\end{gathered} \] They develop a monotone iteration method in presence of upper and lower solutions to the above problem. For an earlier result, see R. Ma, J. Zhang and S. Fu [ibid. 215, No. 2, 415-422 (1997; Zbl 0892.34009)].
Reviewer: Ruyun Ma (Lanzhou)


34B15 Nonlinear boundary value problems for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
47H10 Fixed-point theorems


Zbl 0892.34009
Full Text: DOI


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