Existence of positive solutions for nonlinear dynamic systems with a parameter on a measure chain

Abstract

In this paper, we consider the following dynamic system with parameter on a measure chain $mathbb{T}$, $$displaylines{ u^{DeltaDelta}_{i}(t)+lambda h_{i}(t)f_{i}(u_{1}(sigma(t)), u_{2}(sigma(t)),dots ,u_{n}(sigma(t)))=0,quad tin[a,b], cr alpha u_{i}(a)-eta u^{Delta}_{i}(a)=0,quad gamma u_{i}(sigma(b))+delta u^{Delta}_{i}(sigma(b))=0, }$$ where $i=1,2,dots ,n$. Using fixed-point index theory, we find sufficient conditions the existence of positive solutions.

Keywords

• Dynamic system
• positive solution
• cone
• fixed point
• measure chain.