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There is substantial literature going back to 1965 showing boundedness properties of solutions of the integro-differential equation ... when A is a positive kernel and h is a continuous function using ... In that study there emerges the pair: Integro-differential equation and Supremum norm. In this paper we study qualitative properties of solutions of integral equations using the same inequality and obtain results on Lp solutions. That is, there occurs the pair: Integral equations and Lp norm. The paper also offers many examples showing how to use the Lp idea effectively. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of positive solutions for a class of nonlinear semipositone nth-order boundary value problems. Our approach relies on the Krasnosel'skii fixed point theorem. The result of this paper complement and extend previously known result. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following fourth-order three-point boundary value problem ... where n ∊ [1/3, 1). In spite of sign-changing Green's function, for arbitrary positive integer n (≥ 2), we still obtain the existence of at least n - 1 decreasing positive solutions to the above problem by imposing some suitable conditions on f . The main tool used is the fixed point index theory. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence and uniqueness of convex monotone positive solutions for a boundary value problem of an elastic beam equation with a parameter. The proofs of the main results rely on a fixed point theorem and some properties of eigenvalue problems for a class of general mixed monotone operators. The results can guarantee the existence of a unique convex monotone positive solution and can be applied to construct two iterative sequences for approximating it. Moreover, we present some pleasant properties of convex monotone positive solutions for the boundary value problem dependent on the parameter. Finally, an example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper presents a fixed point theorem utilizing operators and functionals in the spirit of the original Leggett-Williams fixed point theorem which is void of any invariance-like conditions. The underlying sets in the Leggett-Williams fixed point theorem that were defined using the total order of the real numbers are replaced by sets that are defined using an ordering generated by a border-symmetric set, that is, the sets that were defined using functionals in the original Leggett-Williams fixed point theorem are replaced by sets that are defined using operators. [ABSTRACT FROM AUTHOR]

Using the theory of fixed point theorem in cone, this paper presents the existence of positive solutions for the singular m-point boundary value problem {x"(t) + a(t)f(t,x(t), x'(t)) = 0, 0 < t < 1, x'(0) = 0, x(1) = ∑i=1m-2 αix(xi;i), where 0 < ξ1 < ξ2 < ... < ξm-2 < 1, αi ∈ [0, 1), i = 2, ..., m - 2, with 0 < ∑i=1m-2 αi < 1 and f may change sign and may be singular at x = 0 and x' = 0. [ABSTRACT FROM AUTHOR]

In this paper, existence criteria of three positive solutions to the following p-Laplacian functional dynamic equation on time scales {[Φp (uΔ (t))] ∇ + a(t)f(u(t), u(µ(t)00 = 0, t ∈ (0, T), u0(t) = φ(t), t ∈ [-r, 0], - B0 (uΔ (η)) = 0, uΔ(T) = 0, are established by using the well-known Five Functionals Fixed Point Theorem. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of existence and nonexistence of positive solutions for the nonlinear boundary value problem: u(n)(t) + λa(t)f(u(t)) = 0, 0 < t < 1, satisfying three kinds of different boundary value conditions. Our analysis relies on Krasnoselskii's fixed point theorem of cone. An example is also given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of solutions and extrernal solutions for a first order impulsive dynamic inclusion on time scales. By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values. [ABSTRACT FROM AUTHOR]