Positive solutions for second-order nonlinear discrete periodic boundary value problems. (English) Zbl 1240.39016

Ma, Huili; Hu, Chunping

J. Northwest Norm. Univ., Nat. Sci. 46, No. 6, 1-6, 10 (2010).

Summary: A kind of discrete periodic boundary value problems with parameter \(\lambda\) is studied. Under different combinations of sublinearity and superlinearity of nonlinear term \(f\), this paper discusses how the number of positive solutions varies while \(\lambda\) varies, as well as the uniqueness of solutions and the dependence of solutions on the parameter \(\lambda\).

MSC:

39A12	Discrete version of topics in analysis
34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
39A22	Growth, boundedness, comparison of solutions to difference equations
39A10	Additive difference equations

Keywords:

periodic boundary value problem; positive solution; fixed point; Green’s function; positive solutions