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 functional-differential systems via the vector version of Krasnoselskii’s fixed point theorem in cones

2011 ◽  
Vol 27 (2) ◽  
pp. 165-172
Author(s):  
SORIN BUDISAN ◽  
◽  
RADU PRECUP ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Functional Differential Systems ◽  
Existence Of Positive Solutions ◽  
Vector Version ◽  
Functional Differential ◽  
Functional Differential System

We study the existence of positive solutions of the functional-differential system ... (0 < t < 1), subject to linear boundary conditions. We prove the existence of at least one positive solution by using the vector version of Krasnoselskii’s fixed point theorem in cones.

scholarly journals Multiple Positive Symmetric Solutions top-Laplacian Dynamic Equations on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-27
Author(s):  
You-Hui Su ◽  
Can-Yun Huang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Discrete Equations ◽  
Special Cases ◽  
Krasnosel’Skii’S Fixed Point Theorem

This paper makes a study on the existence of positive solution top-Laplacian dynamic equations on time scales&#x1D54B;. Some new sufficient conditions are obtained for the existence of at least single or twin positive solutions by using Krasnosel'skii's fixed point theorem and new sufficient conditions are also obtained for the existence of at least triple or arbitrary odd number positive solutions by using generalized Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem. As applications, two examples are given to illustrate the main results and their differences. These results are even new for the special cases of continuous and discrete equations, as well as in the general time-scale setting.

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 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 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.

Existence of positive solutions for second-order undamped Sturm–Liouville boundary value problems

2016 ◽  
Vol 09 (04) ◽  
pp. 1650089 ◽  
Author(s):  
K. R. Prasad ◽  
L. T. Wesen ◽  
N. Sreedhar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

In this paper, we consider the second-order differential equations of the form [Formula: see text] satisfying the Sturm–Liouville boundary conditions [Formula: see text] where [Formula: see text]. By an application of Avery–Henderson fixed point theorem, we establish conditions for the existence of multiple positive solutions to the boundary value problem.

scholarly journals Positive bounded solutions for nonlinear polyharmonic problems in the unit ball

2017 ◽  
Vol 25 (3) ◽  
pp. 143-153
Author(s):  
Habib Mâagli ◽  
Zagharide Zine El Abidine
Keyword(s):  
Fixed Point ◽  
Positive Integer ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Unit Ball ◽  
Positive Solutions ◽  
Point Theorem ◽  
Bounded Solutions ◽  
Polyharmonic Equation ◽  
Existence Of Positive Solutions

Abstract In this paper, we study the existence of positive solutions for the following nonlinear polyharmonic equation (-∆)mu+λf(x, u) = 0 in B; subject to some boundary conditions, where m is a positive integer, λ is a nonnegative constant and B is the unit ball of ℝn (n ≥ 2). Under some appropriate assumptions on the nonnegative nonlinearity term f(x, u) and by using the Schäuder fixed point theorem, the existence of positive solutions is obtained. At last, examples are given for illustration.

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