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In this paper, we are concerned with the existence of positive solutions of the fully third-order boundary value problem... is continuous. Some inequality conditions on f to guarantee the existence of positive solution are presented. These inequality conditions allow that ƒ(t; x; y; z) may be superlinear or sublinear growth on x, y and z as |(x; y; z)| → 0 and |(x; y; z)| → ∞. [ABSTRACT FROM AUTHOR]

We consider the existence of positive solutions for the nonlinear fractional differential equations boundary value problem -D0+α u(t) = f(t,u(t)), 0 < t < 1, u(0) = u'(0) = u'( 1) = 0, where 2 < α ≤ 3 is a real number, D0+α is the Riemann-Liouville fractional derivative of order α, and f is a given continuous function. Our analysis relies on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]

The existence results of positive ω-periodic solutions are obtained for the second-order functional differential equation with multiple delays u''(t) + a(t)u(t) = f(t,u(t),...,u(t - Tn(t))) ε where a(t) ε C(R) is a positive ω-periodic function, f : R x [0, +∞)n+1 ➝ is a continuous function which is ω-periodic in t, and τ T1(t),...,Tn(t) ε C(R, [0, +∞)) are ω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones. [ABSTRACT FROM AUTHOR]

The existence of positive solutions for Neumann boundary value problem of second-order impulsive differential equations -u''(t) + Mu(t) = f(t, u(t), t ∊ J, t≠ tk, -?u'|t=tk = Ik(u(tk)), k = 1, 2, . . ., m, u'(0) = u'(1) = ?, in an ordered Banach space E was discussed by employing the fixed point index theory of condensing mapping, where M > 0 is a constant, J = [0, 1], f ∊ C(J×K,K), Ik ∊ C(K,K), k = 1, 2, . . ., m, andK is the cone of positive elements in E. Moreover, an application is given to illustrate the main result. [ABSTRACT FROM AUTHOR]

We study the periodic boundary value problem for semilinear fractional differential equations in an ordered Banach space. The method of upper and lower solutions is then extended. The results on the existence of minimal and maximal mild solutions are obtained by using the characteristics of positive operators semigroup and the monotone iterative scheme. The results are illustrated by means of a fractional parabolic partial differential equations. [ABSTRACT FROM AUTHOR]

The existence results of positive solutions are obtained for the fourth-order periodic boundary value problem u(4) = βu" + αu = f(t, u, u"), 0 ≤ t ≤ 1, u(i)(0) = u(i)(1), i = 0, 1, 2, 3, where f : [0, 1] x ℝ+ x ℝ → ℝ+ is continuous, α, β ∈ ℝ, and satisfy 0 < α < ((β/2) + 2π&sup2:) &sup2:, β > -2 π², (α/ π4) + (β/π²) + 1 > 0. The discussion is based on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]

By means of the fixed point theory of strict set contraction operators, we establish a new existence theorem on multiple positive solutions to a singular boundary value problem for second-order impulsive differential equations with periodic boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result. [ABSTRACT FROM AUTHOR]