Triple positive solutions of conjugate boundary value problems II
We shall employ some fixed-point theorems for operators on a cone to obtain existence criteria for (at least) three positive solutions of the following continuous and discrete systems of boundary value problems: (-1)(ni-pi)y(i)((ni))(t) = a(i)(t)h(i)(y(1)(t), y(2)(t),..., y(m)(t)), t is an element of (0, 1), y(i)((j))(0) = 0, 0 less than or equal to j less than or equal to p(i) - 1; y(i)((j))(1) = 0, 0 less than or equal to j less than or equal to n(i) - p(i) - 1, i = 1, 2,...,m and (-1)(n-pi)Delta(n)y(i)(k) = F-i(k, (y) over tilde(1)(k), (y) over tilde(2)(k),..., (y) over tilde(m)(k)), k is an element of {0, 1,..., T}, Delta(j)y(i)(0) = 0, 0 less than or equal to j less than or equal to p(i) - 1; Delta(j)y(i)(T + p(i) + 1) = 0, 0 less than or equal to j less than or equal to n - p(i) - 1, i = 1, 2,..., m, where (y) over tilde(i) = (y(i), Delta y(i),..., Delta(n-1)y(i)), 1 less than or equal to i less than or equal to m. As an application of the results obtained, we establish the existence of (at least) three positive radial solutions for a system, of partial difference equations. Examples are included toillustrate the usefulness of the various criteria obtained. (C) 2000 Elsevier Science Ltd. All rights reserved.
positive solutions systems of boundary value problems radial solutions conjugate boundary conditions