Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A NOTE ON THE EXISTENCE OF SOLUTIONS OF HIGHER-ORDER DISCRETE NONLINEAR STURM-LIOUVILLE TYPE BOUNDARY VALUE PROBLEMS

  • Liu, Yuji (Department of Mathematics, Guangdong University of Business Studies)
  • Published : 2009.01.31
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Abstract

Sufficient conditions for the existence of at least one solution of the boundary value problems for higher order nonlinear difference equations $\{{{{{\Delta^n}x(i-1)=f(i,x(i),{\Delta}x(i),{\cdots},\Delta^{n-2}x(i)),i{\in}[1,T+1],\atop%20{\Delta^m}x(0)=0,m{\in}[0,n-3],}\atop%20\Delta^{n-2}x(0)=\phi(\Delta^{n-1}(0)),}\atop%20\Delta^{n-1}x(T+1)=-\psi(\Delta^{n-2}x(T+1))}\$. are established.

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References

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