Anti-periodic boundary value problems with Riesz–Caputo derivative

Fractional boundary value problems with integral and anti-periodic boundary conditions

In this paper, we consider a class of boundary value problems of fractional differential equations with integral and anti-periodic boundary conditions, which is a new type of mixed boundary condition. By using the contraction mapping principle, Krasnosel’skii fixed point theorem, and Leray-Schauder degree theory, we obtain some results of existence and uniqueness. Finally, several examples are ...

Multiple Positive Solutions for Singular Semipositone Periodic Boundary Value Problems with Derivative Dependence

Periodic Boundary Value Problems on Time Scales

We extend the results concerning periodic boundary value problems from the continuous calculus to time scales. First we use the Schauder fixed point theorem and the concept of lower and upper solutions to prove the existence of the solutions and then we investigate a monotone iterative method which could generate some of them. Since this method does not work on each time scale, a condition cont...

On the solvability of anti-periodic boundary value problems with impulse

Impulsive differential equations, which arise in biology, physics, population dynamics, economics, etc., are a basic tool to study evolution processes that are subjected to abrupt in their states (see [8-12]). Recently, the existence results were extended to anti-periodic boundary value problems for first-order impulsive differential equations [13,14]. Very recently, Wang and Shen [15] investig...

Resonance and Multiplicity in Periodic Boundary Value Problems with Singularity

The paper deals with the boundary value problem u ′′ + k u = g(u) + e(t), u(0) = u(2 ), u(0) = u(2 ), where k ∈ , g : (0,∞) 7→ is continuous, e ∈ [0, 2 ] and lim x→0+ 1 x g(s) ds = ∞. In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.