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Multiple Positive Solutions for Quadratic Integral Equations of Fractional Order [PDF]

Journal of Function Spaces, 2017
In this paper, the existence of multiple positive solutions for a class of quadratic integral equation of fractional order is obtained, by utilizing Avery-Henderson and Leggett-Williams multiple fixed point theorems on cones.
Hui-Sheng Ding, Man-Man Liu, Juan J. Nieto   +2 more
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Monotonic solutions of functional integral and differential equations of fractional order [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2009
The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equations have been studied by J. Banas. Here we are concerned with a singular quadratic functional integral equations.
Ahmed El-Sayed, H. H. G. Hashem
doaj   +17 more sources

Positive solutions for integral boundary value problems of nonlinear fractional differential equations [PDF]

Miskolc Mathematical Notes
In this paper, we consider integral boundary value problems of nonlinear fractional differential equations. Existence results of positive solutions for the problem are obtained based on the Guo-Krasnoselskii theorem and the Five functional fixed point ...
Tawanda Gallan Chakuvinga, Fatma Serap Topal   +1 more
doaj   +5 more sources

A Sum Operator Method for the Existence and Uniqueness of Positive Solutions to a System of Nonlinear Fractional Integral Equations [PDF]

Abstract and Applied Analysis, 2013
This paper is concerned with the existence and uniqueness of positive solutions for a Volterra nonlinear fractional system of integral equations. Our analysis relies on a fixed point theorem of a sum operator.
Jing Wu, Tunhua Wu
doaj   +2 more sources

Positive Solutions of Superlinear Hammerstein Integral Equations in Banach Spaces [PDF]

Journal of Integral Equations and Applications, 1997
The existence of one and two positive solutions of the Hammerstein equation in an ordered Banach space is considered. The essential assumptions on the nonlinear function are uniform continuity on balls, superlinearity with respect to the order, and a (mild) compactness assumption. The proofs make use of the fixed point index for condensing operators; a
Bendong Lou
openalex   +3 more sources

Positive solutions of Volterra integral equations using integral inequalities

Journal of Inequalities and Applications, 2002
The existence of positive solutions of certain special cases of the possibly singular Volterra integral equation is discussed, using Krasnoselskii's fixed point theorem.
O'regan Donal, Meehan Maria
doaj   +3 more sources

Positive Solutions of a Class of Nonlinear Integral Equations and Applications [PDF]

Journal of Integral Equations and Applications, 1992
The authors consider the following nonlinear integral equation \[ u(x)=\lambda\int_ \Omega K(x,y)f(y,u(y))dy,\tag{1} \] where \(\lambda>0\) is a parameter, \(\Omega\) is a bounded closed domain in \(R^ N\), \(K\) is a nonnegative function and \(f(x,u)\) is a reciprocal of a polynomial. Under some additional assumptions, it is shown that (1) has exactly
Lynn Erbe, Dajun Guo, Xinzhi Liu
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Positive Solutions for Systems of Nonlinear Higher Order Differential Equations with Integral Boundary Conditions [PDF]

Abstract and Applied Analysis, 2014
By constructing some general type conditions and using fixed point theorem of cone, this paper investigates the existence of at least one and at least two positive solutions for systems of nonlinear higher order differential equations with integral ...
Yaohong Li, Xiaoyan Zhang
doaj   +2 more sources

Positive solutions for systems of second-order integral boundary value problems [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2013
We investigate the existence and nonexistence of positive solutions of a system of second-order nonlinear ordinary differential equations, subject to integral boundary conditions.
Rodica Luca, Johnny Henderson
doaj   +4 more sources

ON THE NONEXISTENCE OF POSITIVE SOLUTION OF SOME NONLINEAR INTEGRAL EQUATION [PDF]

Demonstratio Mathematica, 2003
Summary: We consider the nonlinear integral equation \[ u(x)= \int_{\mathbb{R}^N} {g(x,y,u(y))\,dy\over|y- x|^\sigma},\quad\text{for all }x\in \mathbb{R}^N,\tag{1} \] where \(\sigma\) is a given positive constant and the given function \(g(x,y,u)\) is continuous and \(g(x,y,u)\geq M{|y|^\beta u^\alpha\over (1+|x|)^\gamma}\) for all \(x,y\in \mathbb{R ...
Nguyen Thanh Long, Dinh Van Ruy
openalex   +3 more sources