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Abstract: In this paper, the existence of positive solutions for a nonlinear general discrete boundary value problem is established. Such results extend and improve some known facts for the two-point and three-point boundary value problems. Particularly, the boundary value conditions can be nonlinear and the method is new. For explaining the main results, some numerical examples are also given. [Copyright &y& Elsevier]

Abstract: This paper deals with the second order three-point boundary value problem The existence and multiplicity of positive solutions are investigated by means of the fixed point theorem in cones. [Copyright &y& Elsevier]

Abstract: In this paper we consider the one-dimensional p-Laplacian boundary value problem on time scales where is p-Laplacian operator, i.e., , . Some new results are obtained for the existence of at least single, twin or triple positive solutions of the above problem by using Krasnosel''skii''s fixed point theorem, new fixed point theorem due to Avery and Henderson and Leggett–Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian boundary value problems on time scales has been studied. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the existence of positive solutions to a n-point nonhomogeneous boundary value problem. By using the Krasnoselskii''s fixed point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of positive solution is established for the n-point nonhomogeneous boundary value problem. [Copyright &y& Elsevier]

Abstract: This paper investigates the existence of positive solutions of singular Dirichlet boundary value problems for second order differential system. A necessary and sufficient condition for the existence of positive solutions as well as positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems. Our nonlinearity may be singular at , , and/or , . [Copyright &y& Elsevier]

Abstract: In this paper we consider the existence of positive solutions of the following boundary value problem: where are the increasing homeomorphism and positive homomorphism and , . We show the sufficient conditions for the existence of positive solutions by using the nome type cone expansion–expression fixed point theorem. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem where λ is a positive parameter. Under various assumptions on a and f we establish intervals of the parameter λ which yield the existence of at least one, at least two, and infinitely many positive solutions of the boundary value problem by using Krasnoselskii''s fixed point theorem of cone expansion–compression type. [Copyright &y& Elsevier]

Abstract: This paper investigates the existence of positive solutions for fourth order singular m-point boundary value problems. Firstly, we establish a comparison theorem, then we define a partial ordering in and construct lower and upper solutions to give a necessary and sufficient condition for the existence of as well as positive solutions. Our nonlinearity may be singular at x, y, and/or . [Copyright &y& Elsevier]

Abstract: In this paper we study the existence of positive solutions of a second-order integral boundary value problems for ordinary differential equations. Our results presented here unify, generalize and substantially improve the existing results in the literature. Moreover, it is worthwhile to point out that our method will dispense with constructing a new Green function. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the existence of positive solutions to the fourth order boundary value problem where , , for are given constants satisfying some suitable conditions. The proofs are based on the fixed point index theorem in cones. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence and nonexistence of positive solutions of the second-order nonlinear dynamic equation , , satisfying either the conjugate boundary conditions or the right focal boundary conditions , where a and f are positive. We show that there exists a such that the above boundary value problem has at least two, one and no positive solutions for , and , respectively. Furthermore, by using the semiorder method on cones of the Banach space, we establish an existence and uniqueness criterion for positive solution of the problem. In particular, such a positive solution of the problem depends continuously on the parameter λ, i.e., is nondecreasing in λ, and . [Copyright &y& Elsevier]

Abstract: This paper is concerned with the exact number of positive solutions for boundary value problems and , where and is a positive parameter. We consider the case in which the nonlinearity f is positive on and changes sign from negative to positive. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the exact number of positive solutions for the boundary value problem and , where and is a positive parameter. We consider the case in which both and change sign exactly once from negative to positive on . [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the existence and multiplicity of positive solutions for nonlinear fractional differential equation boundary value problem: where is a real number, is the standard Riemann–Liouville differentiation, and is continuous. By means of some fixed-point theorems on cone, some existence and multiplicity results of positive solutions are obtained. The proofs are based upon the reduction of problem considered to the equivalent Fredholm integral equation of second kind. [Copyright &y& Elsevier]

Abstract: This paper is concerned with positive solutions of the boundary value problem , where , b is a positive parameter. Assume that f is continuous on (), changes sign from nonpositive to positive, and is nondecreasing in the interval of . The uniqueness results are proved using a time-mapping analysis. [Copyright &y& Elsevier]

Abstract: This paper investigates the existence of positive solutions for 2nth-order () singular sub-linear boundary value problems. A necessary and sufficient condition for the existence of as well as positive solutions is given by constructing lower and upper solutions and with the maximal theorem. Our nonlinearity may be singular at , , and/or . [Copyright &y& Elsevier]

Abstract: In this paper, by using the fixed points of strict-set-contractions, we study the existence of at least one or two positive solutions to the four-point boundary value problem in Banach space E, where θ is zero element of E, , , and . As an application, we also give one example to demonstrate our results. [Copyright &y& Elsevier]

Abstract: In this paper the existence and nonexistence results of positive solutions are obtained for Sturm–Liouville boundary value problem where , , , for , , are constants and satisfy . The discussion is based on the positivity estimation for the Green''s function of associated linear boundary value problem and the fixed point index theory in cones. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence and nonexistence of positive solutions of the nonlinear fourth-order beam equation , , , where is continuous and ζ, η and λ are parameters. We show that there exists a such that the above boundary value problem (BVP) has at least two, one and no positive solutions for , and , respectively. Furthermore, by using the semiorder method on cones of Banach space, we establish a uniqueness criterion for positive solution of the BVP. In particular such a positive solution of the BVP depends continuously on the parameter λ, i.e., is nondecreasing in λ, and for any . [Copyright &y& Elsevier]

Abstract: By using fixed point theorem of cone expansion and compression, this paper investigates the existence of multiple positive solutions for singular boundary value problems of a coupled system of nonlinear ordinary differential equations. [Copyright &y& Elsevier]

In this paper, by means of a new twin fixed-point theorem in a cone, the existence of at least two positive solutions of m-point boundary value problem for second order dynamic equations on time scales is considered. [Copyright &y& Elsevier]

In this paper, some new existence results for positive solutions for a class of singular m-point boundary value problems with parameter be obtained. [Copyright &y& Elsevier]

In this paper, we consider the existence of at least three positive solutions for the 2nth order m-point boundary value problem y(2n)(t)=ft,y(t),y″(t),…,y(2(n−1))(t), 0&les;t&les;1,y(2i)(0)=0, y(2i)(1)=∑lower limit j=1, upper limit m−2 kijy(2i)(ξj), 0&les;i&les;n−1, where kij>0 (i=0,1,…,n−1; j=1,2,…,m−2), 0<ξ1<ξ2<⋯<ξm−2<1. The associated Green''s function for the higher order m-point boundary value problem is first given, and growth conditions are imposed on f which yield the existence of multiple positive solutions by using the Leggett–Williams fixed point theorem. [Copyright &y& Elsevier]

We establish several existence and nonexistence results for the boundary value problem −Δu+K(x)g(u)=λf(x,u)+μh(x) in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in RN, λ and μ are positive parameters, h is a positive function, while f has a sublinear growth. The main feature of this paper is that the nonlinearity g is assumed to be unbounded around the origin. Our analysis shows the importance of the role played by the decay rate of g combined with the signs of the extremal values of the potential K(x) on Ω¯. The proofs are based on various techniques related to the maximum principle for elliptic equations. [Copyright &y& Elsevier]

This paper investigates the structure of solutions of singular boundary value problem with superlinear effect. It is proved that the closure of positive solution set possesses a maximal subcontinuum C (i.e., a maximal closed connected subset of solutions), which comes from (0,θ) and tends to (0,+∞) finally. As a corollary, the existence of multiple positive solutions and the behavior of solutions according to parameter λ are obtained. [Copyright &y& Elsevier]

In this paper the existence results of positive solutions are obtained for fourth-order boundary value problem u(4)+βu″−αu=f(t,u), 0f :[0,1]×R+→R+ is continuous, α,β∈R and satisfy β<2π2, α&ges;−β2/4, α/π4+β/π2<1. [Copyright &y& Elsevier]