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

2021 ◽  
Vol 18 (2) ◽  
pp. 47-60
Author(s):  
B. Kovács
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Differential System ◽  
Point Theorem ◽  
Fourth Order ◽  
Existence Of Positive Solutions ◽  
Cone Expansion And Compression ◽  
Compression Type

Abstract 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.

scholarly journals Positive Solutions of a Singular Nonlocal Fractional Order Differential System via Schauder’s Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xinguang Zhang ◽  
Cuiling Mao ◽  
Yonghong Wu ◽  
Hua Su
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Differential System ◽  
Point Theorem ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Two Parameters

We establish the existence of positive solutions to a class of singular nonlocal fractional order differential system depending on two parameters. Our methods are based on Schauder’s fixed point theorem.

scholarly journals Solvability of a Class of Integral Inclusions

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Ying Chen ◽  
Shihuang Hong
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Nonnegative Function ◽  
Existence Of Positive Solutions ◽  
Multivalued Operators ◽  
Cone Expansion And Compression

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.

scholarly journals Existence of Positive Solution For a Fourth-order Differential System

2021 ◽  
pp. 14-29
Author(s):  
B. Kov´acs
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solution ◽  
Differential System ◽  
Point Theorem ◽  
Fourth Order ◽  
Time And Space

Existence of Positive Solution For a Fourth-order Differential System     where µ > 0 is a constant, and the nonlinear terms f, g may be singular with respect to the time and space variables. By fixed point theorem in cones, the existence is established for singular differential system. The results obtained herein generalize and improve some known results including singular and non-singular cases.

scholarly journals Analysis on Existence of Positive Solutions for a Class Second Order Semipositone Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Yunhai Wang ◽  
Xu Yang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Positive Solution ◽  
Positive Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Existence Of Positive Solutions ◽  
Bounded Below

In this paper, we study the existence of positive solutions of the following second-order semipositone system (see equation 1). By applying a well-known fixed-point theorem, we prove that the problem admits at least one positive solution, if f is bounded below.

scholarly journals The existence of solutions and positive solution of a first - order differential system with initial and multi-point boundary conditions

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1629-1648
Author(s):  
Nguyen Long ◽  
Le Tri ◽  
Le Ngoc
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Differential System ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
Multiplicity Of Positive Solutions

In this paper, we consider a nonlinear differential system with initial and multi - point boundary conditions. The existence of solutions is proved by using the Banach contraction principle or the Krasnoselskii?s fixed point theorem. Furthermore, the existence of positive solutions is also obtained by applying the Guo-Krasnoselskii?s fixed point theorem in cones. As a consequence of the Guo-Krasnosellskii?s fixed point theorem, the multiplicity of positive solutions is established.

scholarly journals Positive Solutions for Discontinuous Systems via a Multivalued Vector Version of Krasnosel’skiĭ’s Fixed Point Theorem in Cones

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 451
Author(s):  
Rodrigo López Pouso ◽  
Radu Precup ◽  
Jorge Rodríguez-López
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Operator ◽  
Positive Solutions ◽  
Point Theorem ◽  
Discontinuous Systems ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Vector Version ◽  
Krasnosel’Skii’S Fixed Point Theorem

We establish the existence of positive solutions for systems of second–order differential equations with discontinuous nonlinear terms. To this aim, we give a multivalued vector version of Krasnosel’skiĭ’s fixed point theorem in cones which we apply to a regularization of the discontinuous integral operator associated to the differential system. We include several examples to illustrate our theory.

scholarly journals Positive solutions of boundary value problems for p-Laplacian fractional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1265-1277 ◽  
Author(s):  
Fatma Fen ◽  
Ilkay Karac ◽  
Ozlem Ozen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Laplacian Operator ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This work is devoted to the existence of positive solutions for nonlinear fractional differential equations with p-Laplacian operator. By using five functionals fixed point theorem, the existence of at least three positive solutions are obtained. As an application, an example is presented to demonstrate our main result.

scholarly journals EXISTENCE OF POSITIVE SOLUTIONS FOR SUPERLINEAR SEMIPOSITONE $m$-POINT BOUNDARY-VALUE PROBLEMS

2003 ◽  
Vol 46 (2) ◽  
pp. 279-292 ◽  
Author(s):  
Ruyun Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
The Fixed Point Theorem

AbstractIn this paper we consider the existence of positive solutions to the boundary-value problems\begin{align*} (p(t)u')'-q(t)u+\lambda f(t,u)\amp=0,\quad r\ltt\ltR, \\[2pt] au(r)-bp(r)u'(r)\amp=\sum^{m-2}_{i=1}\alpha_iu(\xi_i), \\ cu(R)+dp(R)u'(R)\amp=\sum^{m-2}_{i=1}\beta_iu(\xi_i), \end{align*}where $\lambda$ is a positive parameter, $a,b,c,d\in[0,\infty)$, $\xi_i\in(r,R)$, $\alpha_i,\beta_i\in[0,\infty)$ (for $i\in\{1,\dots m-2\}$) are given constants satisfying some suitable conditions. Our results extend some of the existing literature on superlinear semipositone problems. The proofs are based on the fixed-point theorem in cones.AMS 2000 Mathematics subject classification: Primary 34B10, 34B18, 34B15

Positive solutions of superlinear boundary value problems

1981 ◽  
Vol 88 (1-2) ◽  
pp. 17-24 ◽  
Author(s):  
Heinrich Voss
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Existence Of Positive Solutions ◽  
Image Position

SynopsisUsing a fixed point theorem on operators expanding a cone in a Banach space we prove the existence of positive solutions of superlinear boundary value problemsAt the same time we get bounds (or even inclusions) of positive solutions.

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