摘要
By fixed point index theory and a result obtained by Amann, existence of the solution for a class of nonlinear operator equations x = Ax is discussed. Under suitable conditions, a couple of positive and negative solutions are obtained. Finally, the abstract result is applied to nonlinear Sturm-Liouville boundary value problem, and at least four distinct solutions are obtained.
By fixed point index theory and a result obtained by Amann, existence of the solution for a class of nonlinear operator equations x = Ax is discussed. Under suitable conditions, a couple of positive and negative solutions are obtained. Finally, the abstract result is applied to nonlinear Sturm-Liouville boundary value problem, and at least four distinct solutions are obtained.
基金
. This work is supported by the WNSFC(60304003, 10371066)
the NSF of Shandong Province(Z2003A01, Y02P01)
and the doctoral Foundation of Shandong Province(03B5092)
