Nonnegative solutions to boundary value problems for nonlinear first and second order ordinary differential equations

On the existence of positive solutions of ordinary differential equations

“…The BVP (1.1), (1.2) arises in many different areas of applied mathematics and physics; see [1-3, 6, 12, 13] for some references along this line. Additional existence results may be found in [4,7,8,10,11]. Our purpose here is to give an existence result for positive solutions to the BVP (1.1), (1.2), assuming that / is either superlinear or sublinear.…”

Boundary value problems for systems of differential equations

“…We improve on some results of Bebernes [2] and of Gufstafson and Schmitt [5]. In Corollary 2.8 we apply our results to show that the condition f(x,y) ^ -ay for some a > 0 and all y ^ 0 in Santanilla [11,Theorem 3.2] can be relaxed (see [11] for further discussion and references). In Section 3 we consider (1)(2)(3) y" = f(*,y,y') * e [ o , i ] with the periodic, Picard and Neumann boundary conditions respectively.…”

“…In Section 2 we consider the problem (11) y' = f(x,y), *e[0,i] (1)(2) where / : [0,1] x R n -> R n is continuous and /(0,-) = /(I,-). A solution y is a continuously differentiable R n -valued function which satisfies (1.1) everywhere in [0,1] and the boundary conditions (1.2).…”

“…A solution y is a continuously differentiable R n -valued function which satisfies (1.1) everywhere in [0,1] and the boundary conditions (1.2). We use shooting arguments combined with Brouwer degree theory (see [1] and [10]) in contrast to the coincidence degree used in [11] and the Schauder degree used in [2]. We improve on some results of Bebernes [2] and of Gufstafson and Schmitt [5].…”

On the existence of positive solutions of nonlinear second order differential equations

“…There has recently been an increased interest in studying the existence of positive solutions of the following boundary value problem in the last fifteen to twenty-five years; see, for example, Bandle, Coffman and Marcus [1], Bandle and Kwong [2], Coffman and Marcus [3], H. Dang and K. Schmit [4], Erbe [6], Erbe, Hu and Wang [7], Erbe and Wang [8], Garaizar [9], Iffland [11], Santanilla [13], Wang [14] and Wong [15].…”