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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]

In this paper, we are concerned with the existence of positive solutions of the fully third-order boundary value problem ..., where f: [0, 1] x ℝ+ x ℝ+ x ℝ → ℝ is continuous. Some inequality conditions on f to guarantee the existence of positive solution are presented. These inequality conditions allow that f (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]

By using monotone iterative technique and operator semigroup theorem, we consider the existence of mild solutions for a class of nonlocal semi-linear evolution equation with not instantaneous impulses in ordered Banach spaces. Finally, an example is given to show the existence results. [ABSTRACT FROM AUTHOR]

In this article, we use a monotone iterative technique based on the presence of lower and upper solutions to discuss the existence of mild solutions for the initial value problem of the impulsive time fractional order partial differential equation of Volterra type in an ordered Banach space E where D0q is the Caputo fractional derivative of order q, 0 < q < 1, A : D(A) ⊂ E → E is a closed linear operator and -A is a generator of equicontinuous C0-semigroup, f ∈ C(J×E×E;E), J = [0, a], a > 0 is a constant, T is a Volterra integral operator, 0 < t1 < t2 < ⋯ < tm < a, Ik ∈ C(E,E), k = 1, 2, ∈, m and x0 ∈ E. Under wide monotone conditions and the noncompactness measure condition of nonlinearity f, we obtain the existence of extremal mild solutions and unique mild solution between lower and upper solutions. The results obtained generalize the recent conclusions on this topic. An example is also given to illustrate that our results are valuable. [ABSTRACT FROM AUTHOR]