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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]

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]

In this article, we are concerned with the initial value problem of fractional stochastic evolution equations in real separable Hilbert spaces. The existence of saturated mild solutions and global mild solutions is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions by using a-order fractional resolvent operator theory, the Schauder fixed point theorem and piecewise extension method. Furthermore, the continuous dependence of mild solutions on initial values and orders as well as the asymptotical stability in p-th moment of mild solutions for the studied problem have also been discussed. The results obtained in this paper improve and extend some related conclusions on this topic. An example is also given to illustrate the feasibility of our abstract results. [ABSTRACT FROM AUTHOR]

The aim of this article is to study the existence and uniqueness of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions. The discussions are based on analytic semigroup theory and fixed point theorems. An example illustrates the main results. [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]

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]