UNCOUNTABLY MANY BOUNDED POSITIVE SOLUTIONS FOR A SECOND ORDER NONLINEAR NEUTRAL DELAY PARTIAL DIFFERENCE EQUATION

作者：Liu, Z.^*; Wu, Z.; Ume, J. S.; Kang, S. M.

来源：Bulletin of the Iranian Mathematical Society, 2015, 41(2): 389-405.

• Uncountably many bounded positive solutions
• second order nonlinear neutral delay partial difference equation
• Banach fixed point theorem

In this paper we consider the second order nonlinear neutral delay partial difference equation
Delta(n)Delta(m)(x(m,n) + a(m,n)x(m-k,n-t)) + f(m,nx(m-tau,n-sigma)) = b(m,n),m >= m(0), n >= n(0).
Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation. Three nontrivial examples are given to illustrate the advantages of our results.

• 出版日期2015-5
• 单位辽宁师范大学