On the existence of positive solutions of ordinary differential equations

Abstract

Abstract. We study the existence of positive solutions of the equation u" + a{t)f{u) = 0 with linear boundary conditions. We show the existence of at least one positive solution if / is either superlinear or sublinear by a simple application of a Fixed Point Theorem in cones.

Minimal Positive Solutions to Some Singular Second-Order Differential Equations

“…Under the conditions of superlinearity, semilinearity, delay, etc., some well-known results have been obtained with x + f t x = 0 (see, e.g., [1,3,6,9]). …”

Solving singular second-orderinitial/boundary value problems in reproducing kernel Hilbert space

“…Such problems have been investigated in many researches. Specially, the existence and uniqueness of the solution of (1.1) have been discussed in [1][2][3][4][5]. And in recent years, there are also a large number of special-purpose methods are proposed to provide accurate numerical solutions of the special form of (1.1), such as collocation methods [6], finite-element methods [7], Galerkin-wavelet methods [8], variational iteration method [9], spectral methods [10], finite difference methods [11], etc.…”

Existence results of Brezis-Browder type for systems of Fredholm integral equations

“…A solution u of (1.1) (or (1.2)) is said to be of constant sign if for each 1 ≤ i ≤ n, we have Particular cases of (1.3) are also considered in [1][2][3]. The reader is referred to the monographs [ [4,5], and the references cited therein] for the related literature.…”