Three symmetric solutions of Lidstone boundary value problems for difference and partial difference equations
We consider the boundary value problem Delta(2m)y(k - m) = f (y(k), Delta(2)y(k - 1),..., Delta(y)(2i)(k - i),..., Delta(2(m-1)) y(k - (m-1))), k is an element of {a + 1,..., b+1}, Delta(2i)y(a + 1 - m) = Delta(y)(2i)(b + 1 + m - 2i) = 0, 0 less than or equal to i less than or equal to m - 1, where m greater than or equal to 1 and (-1)(m)f : R-m --> [0,infinity) is continuous. By using Amann and Leggett-Williams' fixed-point theorems, we develop growth conditions on f so that the boundary value problem has triple positive symmetric solutions. The results obtained are then applied in the investigation of radial solutions for certain partial difference equation subject to Lidstone type conditions. (C) 2003 Elsevier Science Ltd. All rights reserved.
boundary value problems partial difference equations difference equations positive symmetric solutions