Positive solutions of second-order problem with dependence on derivative in nonlinearity under Stieltjes integral boundary condition

摘要

In this paper, we investigate the second-order problem with dependence onderivative in nonlinearity and Stieltjes integral boundary conditionwhere f : [0, 1] × R+ × R+ ! R+ is continuous and a[u] is a linear functional. Someinequality conditions on nonlinearity f and the spectral radius conditions of linearoperators are presented that guarantee the existence of positive solutions to the problemby the theory of fixed point index on a special cone in C1[0, 1]. The conditions allow thatf (t, x1, x2) has superlinear or sublinear growth in x1, x2. Some examples are given toillustrate the theorems respectively under multi-point and integral boundary conditionswith sign-changing coefficients.