Positive Solutions of a Singular Fractional Boundary Value Problem with r-Laplacian Operators

We investigate the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations with r-Laplacian operators and nonnegative singular nonlinearities depending on fractional integrals, supplemented with nonlocal uncoupled boundary conditions which contain Riemann–Stieltjes integrals and various fractional derivatives. In the proof of our main results we apply the Guo–Krasnosel’skii fixed point theorem of cone expansion and compression of norm type.

Existence of Positive Solution for a Singular Fourth–Order Differential System

This paper investigates the existence of positive solutions for a fourth-order differential system using a fixed point theorem of cone expansion and compression type.

A Constructive Approach About the Existence of Positive Solutions for Minkowski Curvature Problems

In this paper, we give an existence theorem about positive solutions for the Dirichlet boundary value problem of one dimensional Minkowski curvature equations. We apply the theorem to one parameter family of problems to investigate a constructive method for numerical range of parameters where positive solutions exist. Moreover, we establish a nonexistence theorem of positive solutions for the corresponding one parameter family of problems. The coefficient function may be singular at the boundary and nonlinear term satisfies a sublinear growth condition. Main argument for the proof of existence theorem is employed by Krasnoselskii’s theorem of cone expansion and compression. We give a numerical algorithm and various examples to illustrate numerical information about ranges of the existence and nonexistence parameters which have been given only in a theoretical manner so far.

Positive solutions of nth-order impulsive differential equations with integral boundary conditions

This paper is concerned with the existence and nonexistence of positive solutions of nth-order impulsive boundary value problem with integral boundary conditions. The fixed point theorem of cone expansion and compression is used to investigate the existence of at least one positive solution. Also, an example is given to illustrate the effective of our results.

Multiple Solutions of Boundary Value Problems fornth-Order Singular Nonlinear Integrodifferential Equations in Abstract Spaces

The authors discuss multiple solutions for thenth-order singular boundary value problems of nonlinear integrodifferential equations in Banach spaces by means of the fixed point theorem of cone expansion and compression. An example for infinite system of scalar third-order singular nonlinear integrodifferential equations is offered.

Existence and Nonexistence of Positive Solutions for a Higher-Order Three-Point Boundary Value Problem

This paper is concerned with the existence and nonexistence of positive solutions for a nonlinear higher-order three-point boundary value problem. The existence results are obtained by applying a fixed point theorem of cone expansion and compression of functional type due to Avery, Henderson, and O’Regan.

Positive Solutions for a Nonlinear Higher Order Differential System with Coupled Integral Boundary Conditions

We investigate the existence of positive solutions for a nonlinear higher order differential system, where the differential system is coupled not only in the differential system but also through the boundary conditions. By constructing a special cone and using the fixed point theorem of cone expansion and compression of norm type, the existence of single and multiple positive solutions is established. As an application, we give some examples to demonstrate our results.

Some Existence Results of Positive Solution to Second-Order Boundary Value Problems

We study the existence of positive and monotone solution to the boundary value problemu′′(t)+f(t,u(t))=0,0⩽t⩽1,u(0)=ξu(1),u'(1)=ηu'(0), whereξ,η∈(0,1)∪(1,∞). The main tool is the fixed point theorem of cone expansion and compression of functional type by Avery, Henderson, and O’Regan. Finally, four examples are provided to demonstrate the availability of our main results.

Solvability of a Class of Integral Inclusions

This paper presents sufficient conditions for the existence of positive solutions for a class of integral inclusions. Our results are obtained via a new fixed point theorem for multivalued operators developed in the paper, in which some nonnegative function is used to describe the cone expansion and compression instead of the classical norm-type, and lead to new existence principles.

Existence of Positive Solution for Multi-Point Sturm-Liouville Boundary Value Problem

Multi-point boundary value problem is studied in this paper. With the condition that nonlinear term is superlinear or sublinear, it is proved that there exists at least one positive solution to multi-point Sturm-Liouville boundary value problem by using the fixed-point theorem concerning cone expansion and compression of norm type.