Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales

الملخص EN

In this paper, we study a general second-order m-point boundary value problem for nonlinear singular dynamic equation on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0, t∈(0,1)?, u(ρ(0))=0, u(σ(1))=∑i=1m-2αiu(ηi).

This paper shows the existence of multiple positive solutions if f is semipositone and superlinear.

The arguments are based upon fixed-point theorems in a cone.