scholarly journals Multiple Positive Solutions of Second-Order Nonlinear Difference Systems with Repulsive Singularities

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Shengjun Li ◽  
Fang Zhang
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Difference Systems ◽  
Nonlinear Alternative ◽  
Existence Of Positive Solutions ◽  
Alternative Principle

We study the existence of positive solutions for second-order nonlinear repulsive singular difference systems with periodic boundary conditions. Our nonlinearity may be singular in its dependent variable. The proof of the main result relies on a fixed point theorem in cones and a nonlinear alternative principle of Leray-Schauder; the result is applicable to the case of a weak singularity as well as the case of a strong singularity. An example is given; some recent results in the literature are improved and generalized.

scholarly journals Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Shengjun Li ◽  
Li Liang ◽  
Zonghu Xiu
Keyword(s):  
Boundary Condition ◽  
Differential Equations ◽  
Positive Solutions ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Nonlinear Differential Equations ◽  
Nonseparated Boundary Conditions ◽  
Nonlinear Alternative ◽  
Existence Of Positive Solutions ◽  
Alternative Principle

We study the existence of positive solutions for second-order nonlinear differential equations with nonseparated boundary conditions. Our nonlinearity may be singular in its dependent variable. The proof of the main result relies on a nonlinear alternative principle of Leray-Schauder. Recent results in the literature are generalized and significantly improved.

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

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Zhaocai Hao ◽  
Tanggui Chen
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Nonlinear Alternative ◽  
Existence Of Positive Solutions ◽  
Alternative Principle

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.

scholarly journals Positive Solutions to Periodic Boundary Value Problems for Four-Order Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Huantao Zhu ◽  
Zhiguo Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Periodic Boundary Value Problems

We apply fixed point theorem in a cone to obtain sufficient conditions for the existence of single and multiple positive solutions of periodic boundary value problems for a class of four-order differential equations.

scholarly journals Multiplicity of positive solutions for second order Sturm-Liouville boundary value problems

2016 ◽  
Vol 25 (2) ◽  
pp. 215-222
Author(s):  
K. R. PRASAD ◽  
◽  
N. SREEDHAR ◽  
L. T. WESEN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Sturm Liouville ◽  
Multiplicity Of Positive Solutions

In this paper, we develop criteria for the existence of multiple positive solutions for second order Sturm-Liouville boundary value problem, u 00 + k 2u + f(t, u) = 0, 0 ≤ t ≤ 1, au(0) − bu0 (0) = 0 and cu(1) + du0 (1) = 0, where k ∈ 0, π 2 is a constant, by an application of Avery–Henderson fixed point theorem.

scholarly journals Positive solutions for singular semipositone nonlinear fractional differential system

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 169-179
Author(s):  
Rim Bourguiba ◽  
Faten Toumi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Nonlinear Alternative ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, under suitable conditions we employ the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel?skii fixed point theorem to show the existence of positive solutions for a system of nonlinear singular Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to integral boundary conditions. Some examples are given to illustrate our main results.

scholarly journals Multiple Positive Solutions of a Second Order Nonlinear Semipositonem-Point Boundary Value Problem on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Chengjun Yuan ◽  
Yongming Liu
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Dynamic Equation ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Point Boundary

In this paper, we study a general second-orderm-point boundary value problem for nonlinear singular dynamic equation on time scalesuΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0,t∈(0,1)𝕋,u(ρ(0))=0,u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions iffis semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone.

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