Multiple symmetric positive solutions for discrete Lidstone boundary value problems. (English) Zbl 0969.39003

Henderson, Johnny

Dyn. Contin. Discrete Impulsive Syst. 7, No. 4, 577-584 (2000).

The difference equation \[ (-1)^m\Delta^{2m} y(t-m)= f\bigl(y(t) \bigr), \quad t\in \{1,2, \dots, T+1\} \] is considered subject to \(\Delta^{2i} y(-m+1)=0\), \(0\leq i\leq m-1\), and \(\Delta^{2j} y(T+m+1-2j)=0\), \(0\leq j\leq m-1\). Under certain growth conditions for the positive function \(f\) the existence of at least three symmetric positive solutions is proved by means of a fixed point theorem due to R. W. Leggett and L. R. Williams [Indiana Univ. Math. J. 28, 673-688 (1979; Zbl 0421.47033)].

Reviewer: Lothar Berg (Rostock)

MSC:

39A11

Stability of difference equations (MSC2000)

Keywords:

nonlinear difference equations; multiple symmetric positive solutions; discrete Lidstone boundary value problems; fixed point theorem

Citations:

Zbl 0421.47033