Utilizing the theory of fixed point index for compact maps, we establish new results on the existence of positive solutions for a certain third order boundary value problem. The boundary conditions that we study are of nonlocal type, involve Stieltjes integrals and are allowed to be nonlinear.
In this paper we consider the existence, multiplicity, and nonexistence of positive solutions to fractional differential equation with integral boundary conditions. Our analysis relies on the fixed point index.
In this paper, we prove some multiplicity results for sign-changing solutions of an operator equation in an ordered Banach space. The methods to show the main results of the paper are to associate a fixed point index with a strict upper or lower solution. The results can be applied to a wide variety of boundary value problems to obtain multiplicity results for sign-changing solutions.
This paper deals with the existence of positive ω-periodic solutions for the neutral functional differential equation with multiple delays (u(t) − cu(t − δ))′ + a(t)u(t) = f(t, u(t − τ1), . . . , u(t − τn)). The essential inequality conditions on the existence of positive periodic solutions are obtained. These inequality conditions concern with the relations of c and the coefficient function a(t), and the nonlinearity f(t, x1, . . . , xn). Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.