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Existence of positive solutions for certain nonlinear partial difference equations

Authors
Journal
Mathematical and Computer Modelling
0895-7177
Publisher
Elsevier
Publication Date
Volume
38
Identifiers
DOI: 10.1016/s0895-7177(03)90091-4
Keywords
  • Partial Difference Equations
  • Positive Solutions
  • Fixed-Point Theorem
Disciplines
  • Mathematics

Abstract

Abstract In this paper, we consider nonlinear partial difference equations of the form Δ n hΔ m r (x m,n − cx m−k,n−l) + (−1) h+r+1Pm,nƒ(x m−τ,n−δ) = 0 , where cϵ R, h,r,k,l ϵ N +, τ,δ ϵ N, { Pm,n} m = m 0 ∞,∞ , n = n 0 is a double sequence of real numbers and ƒ ϵ C( R, R). We obtain sufficient conditions for the existence of positive solutions of this equation using Knaster's fixed-point theorem.

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