Extensions of Schauder\u27s and Darbo\u27s Fixed Point Theorems

In this paper, some new extensions of Schauder\u27s and Darbo\u27s fixed point theorems are given. As applications of the main results, the existence of global solutions for first-order nonlinear integro-differential equations of mixed type in a real Banach space is investigated

Existence of Positive Solutions for Multi-Point Boundary Value Problems on Infinite Intervals in Banach Spaces

We investigate the positive solutions of a class of second-order nonlinear singular differential equations with multi-point boundary value conditions on an infinite interval in Banach spaces. The tools we used are the cone theory and Mönch fixed point theorem and a monotone iterative technique. An example is also given to demonstrate the applications of our results, which include and extend some existing results

Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments

We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments Dαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),20,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and  η∈(0,1), where Dα is the standard Riemann-Liouville derivative, f:[0,∞)→[0,∞) is continuous, f(0)>0, h :[0,1]→(−∞,+∞), and a(t) is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results

The Unique Solution for Sequential Fractional Differential Equations with Integral Multi-Point and Anti-Periodic Type Boundary Conditions

In this paper, we obtain the existence of the unique solution of anti-periodic type (anti-symmetry) integral multi-point boundary conditions for sequential fractional differential equations. We apply the Banach contraction mapping principle to get the desired results. Our results specialize and extend some existing results

The Existence of Positive Solutions for Singular Impulse Periodic Boundary Value Problem

We obtain new result of the existence of positive solutions of a class of singular impulse periodic boundary value problem via a nonlinear alternative principle of Leray-Schauder. We do not require the monotonicity of functions in paper (Zhang and Wang, 2003). An example is also given to illustrate our result

Existence and Uniqueness of Positive Solutions for Singular Nonlinear Fractional Differential Equation via Mixed Monotone Operator Method

In this article, we discuss the existence and uniqueness of positive solution for a class of singular fractional differential equations, where the nonlinear term contains fractional derivative and an operator. By applying the fixed point theorem in cone, we get the existence and uniqueness of positive solutions for the fractional differential equation. Moreover, we give an example to demonstrate our main result

Some Existence Results for High Order Fractional Impulsive Differential Equation on Infinite Interval

In this paper, we consider the high order impulsive differential equation on infinite interval D0+αut+ft,ut,J0+βut,D0+α−1ut=0, t∈0,∞∖tkk=1m△utk=Ikutk, t=tk,k=1,…,mu0=u′0=⋯=un−20=0,D0+α−1u∞=u0 By applying Schauder fixed points and Altman fixed points, we obtain some new results on the existence of solutions. The nonlinear term of the equation contains fractional integral operator Jβut and lower order derivative operator D0+α−1ut. An example is presented to illustrate our results

The Unique Solution for Sequential Fractional Differential Equations with Integral Multi-Point and Anti-Periodic Type Boundary Conditions

In this paper, we obtain the existence of the unique solution of anti-periodic type (anti-symmetry) integral multi-point boundary conditions for sequential fractional differential equations. We apply the Banach contraction mapping principle to get the desired results. Our results specialize and extend some existing results