Positive Solutions for Nonlinear Second Order Impulsive Differential Systems with Two Parameters

Abstract:

The paper presents a study of the existence of positive solutions for a class of nonlinear second order impulsive differential systems with two parameters and the nonexistence of positive solutions,where the nonlinear terms have different properties and their coefficients a1(t),a2(t) are LPintegrable.By applying the theory of the fixed point index and constructing a special cone,the existence theorem of positive solutions is proved when parameters λ and μ have different conditions,and the nonexistence theorem of positive solutions is proved while λ is sufficiently small.

Key words:positive solution; boundary value problem; fixed point index; cone