Periodic boundary value problems for nonlinear impulsive fractional differential equation

In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle

Triple positive solutions for second-order four-point boundary value problem with sign changing nonlinearities

In this paper, we study the existence of triple positive solutions for second-order four-point boundary value problem with sign changing nonlinearities. We first study the associated Green's function and obtain some useful properties. Our main tool is the fixed point theorem due to Avery and Peterson. The results of this paper are new and extent previously known results

Existence of multiple positive solutions of higher order multi-point nonhomogeneous boundary value problem

In this paper, by using the Avery and Peterson fixed point theorem, we establish the existence of multiple positive solutions for the following higher order multi-point nonhomogeneous boundary value problem $u^{(n)}(t) + f(t,u(t),u'(t),\ldots,u^{(n-2)}(t)) = 0, t\in (0,1)$, $u(0)= u'(0)=\cdots=u^{(n-3)}(0)=u^{(n-2)}(0)=0, u^{(n-2)}(1)-\sum_{i=1}^{m} a_i u^{(n-2)}(\xi_i)=\lambda$, where $n\ge3$ and $m\ge1$ are integers, $00$ for $1\le i\le m$ and $\sum_{i=1}^{m} a_i\xi_i<1$, $f(t,u,u',\cdots,u^{(n-2)})\in C([0,1]\times[0,\infty)^{n-1}, [0,\infty))$. We give an example to illustrate our result

Existence of solutions for fourth order differential equation with four-point boundary conditions

AbstractIn this paper we investigate the existence of solutions of a class of four-point boundary value problems for a fourth order ordinary differential equation. Our analysis relies on a nonlinear alternative of Leray–Schauder type

Green's function and positive solutions of a singular nth-order three-point boundary value problem on time scales

In this paper, we investigate the existence of positive solutions for a class of singular $n$th-order three-point boundary value problem. The associated Green's function for the boundary value problem is given at first, and some useful properties of the Green's function are obtained. The main tool is fixed-point index theory. The results obtained in this paper essentially improve and generalize some well-known results

Existence of positive solutions for nth-order boundary value problem with sign changing nonlinearity

In this paper, we investigate the existence of positive solutions for singular $n$th-order boundary value problem $u^{(n)}(t)+a(t)f(t,u(t))=0,\quad 0\le t\le1,$ $u^{(i)}(0)=u^{(n-2)}(1)=0,\quad 0\le i\le n-2,$ where $n\ge2$, $a\in C((0,1),[0,+\infty))$ may be singular at $t=0$ and (or) $t=1$ and the nonlinear term $f$ is continuous and is allowed to change sign. Our proofs are based on the method of lower solution and topology degree theorem

Positive solutions for nonlinear semipositone nth-order boundary value problems

In this paper, we investigate the existence of positive solutions for a class of nonlinear semipositone $n$th-order boundary value problems. Our approach relies on the Krasnosel'skii fixed point theorem. The result of this paper complement and extend previously known result

Impulsive periodic boundary value problems for fractional differential equation involving Riemann–Liouville sequential fractional derivative

AbstractIn this paper, we investigate the existence of solutions of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann–Liouville sequential fractional derivative by using monotone iterative method. An example is presented to illustrate our main result

Existence of Positive Solutions for a Functional Fractional Boundary Value Problem

We study the existence of positive solutions for a boundary value problem of fractional-order functional differential equations. Several new existence results are obtained

New results concerning the exponential stability of delayed neural networks with impulses

AbstractEmploying the matrix measure approach and Lyapunov function, the author studies the global exponential stability of delayed neural networks with impulses in this paper. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point for such delayed neural networks with impulses. Finally, three examples are given to show the effectiveness of the results obtained here