Multiple positive solutions of a discrete second order conjugate problem. (English) Zbl 0959.39006

Avery, Richard I.; Peterson, Allan C.

Panam. Math. J. 8, No. 3, 1-12 (1998).

Summary: We are concerned with the discrete second-order conjugate boundary value problem \[ \Delta^2x(t- 1)+ f(x(t))= 0,\quad x(a)= 0= x(b+ 2). \] Under various assumptions on \(f\) we prove the existence of three positive solutions of this boundary value problem applying the fixed point theorem of Y. Sun and J. Sun [J. Math. Anal. Appl. 148, No. 2, 431-439 (1990; Zbl 0709.47052)] for weakly inward operators.

MSC:

39A11

Stability of difference equations (MSC2000)

Keywords:

difference equations; Green’s function; fixed points; positive solutions; discrete second-order conjugate boundary value problem

Citations:

Zbl 0709.47052