摘要
设E是实Banach空间，P是E中的锥，在E中引入半序：u≤v(u，v∈E)，如果u-u∈P。这时，称E是有序Banach空间，记做(E，P)。若存在正数N，对任何的u≥u≥θ(θ表E中的零元)，
In this paper we have proved the following two theorems on the existence of positive solutions of nonlinear integral equations. We first consider Hammerstein nonlinear integral equationwhere G is a bounded closed domain in Euclidean space R , K(X, y) is a non-negtive continuous function on G×G.Theorem i. Suppose that the following three conditions are satisfied.(iii) K(x, y) is a loccaly positive function on G×G;Then the equation (5) has a non-negtive continuous solution u(x) which does not equal zero identically.we next consider Urysohn nonlinear integral equationwhere i(x, y, t)is a non-negtive continuous function on G×G× (0, + ∞). Theorem 2.Suppose that the following two conditions are satisfied.Then the equation(3)has a non-negtive continuous solution u(x) which does not equal zero identically.
