The initial value problem of convex conservation laws, which includes the famous Burgers’ (inviscid) equation, plays an important rule not only in theoretical analysis for conservation laws, but also in numerical computations for various numerical methods. For example, the initial value problem of the Burgers’ equation is one of the most popular benchmarks in testing various numerical methods. ...

This paper concerned with the existence of solutions of anti-periodic boundary value problems for impulsive differential equations with φ-Laplacian operator. Firstly, the definition a pair of coupled lower and upper solutions of the problem is introduced. Then, under the approach of coupled upper and lower solutions together with Nagumo condition, we prove that there exists at least one solutio...

Fractional differential equations arise in various areas of science and engineering, such as physics, mechanics, chemistry, and engineering. The fractional order models become more realistic and practical than the classical integer models. Due to their applications, fractional differential equations have gained considerable attentions; one can see [1–14] and references therein. Anti-periodic bo...

Abstract: In this paper we study a periodic boundary value problem of first order nonlinear differential equations with maxima and discuss the existence and approximation of the solutions. The main result relies on the Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014) in a partially ordered normed linear space. At the end, we give an example to illustrate th...

‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...

this paper studies a fractional boundary value problem of nonlineardifferential equations of arbitrary orders. new existence and uniquenessresults are established using banach contraction principle. other existenceresults are obtained using schaefer and krasnoselskii fixed point theorems.in order to clarify our results, some illustrative examples are alsopresented.

In this paper, we study the differential equation with the periodic boundary value u′′(t) = f(t, u(t), u′(t)), t ∈ [0, 2π] u(0) = u(2π), u′(0) = u′(2π). The existence of solutions to the periodic boundary problem above with appropriate conditions is proved by using an upper and lower solution method.