Existence of positive solution for second-order nonlinear discrete system with parameter*,1

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Abstract

This paper is concerned with the following discrete system,Δ2ui(k)+λhi(k)fi(u1(k),u2(k),,un(k))=0,k[0,T],i=1,2,n,ui(0)=ui(T+2)=0,i=1,2,,n.By using the theory of the fixed-point index, sufficient conditions are obtained for the existence of positive solution to the above system.

Keywords

Discrete system
Positive solution
Cone
Fixed point

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*

Supported by the Key Research and Development Program for Outstanding Groups of Lanzhou University of Technology.

1

Supported by the NNSF of China (10171040), the NSF of Gansu Province of China (ZS011-A25-007-Z) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of Ministry of Education of China.