scholarly journals Transformation technique, fixed point theorem and positive solutions for second-order impulsive differential equations with deviating arguments

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Xuemei Zhang ◽  
Meiqiang Feng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Positive Solutions ◽  
Point Theorem ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Transformation Technique ◽  
Deviating Arguments

scholarly journals Existence and Uniqueness of Positive Solutions to Nonlinear Second Order Impulsive Differential Equations with Concave or Convex Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Lingling Zhang ◽  
Chengbo Zhai
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Point Boundary

Using a new fixed point theorem of generalized concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions to nonlinear two-point boundary value problems for second-order impulsive differential equations with concave or convex nonlinearities.

scholarly journals Positive periodic solutions for second order impulsive differential equations

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Jianhua Shen ◽  
Weibing Wang ◽  
Zhimin He
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Impulsive Differential Equations ◽  
Existence Results ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Continuous Equation

AbstractThe existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using fixed point theorem in cone, new existence results of positive periodic solutions are obtained without assuming the existence of positive periodic solutions of the corresponding continuous equation.

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 Multiplicity of positive periodic solutions to second order differential equations

2006 ◽  
Vol 73 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O'Regan ◽  
R. P. Agarwal
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Second Order Differential Equations

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

scholarly journals PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

2010 ◽  
Vol 82 (3) ◽  
pp. 437-445 ◽  
Author(s):  
JIFENG CHU ◽  
ZIHENG ZHANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Schauder’S Fixed Point Theorem ◽  
Positive Periodic Solutions ◽  
Singular Differential Equations ◽  
Attractive Case

AbstractIn this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

scholarly journals Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yuanhong Wei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Function Space ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Second Order Differential Equations

We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained.

One-Signed Harmonic Solutions and Sign-Changing Subharmonic Solutions to Scalar Second Order Differential Equations

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Alberto Boscaggin
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Point Theorem ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Subharmonic Solutions

AbstractUsing a recent modified version of the Poincaré-Birkhoff fixed point theorem [19], we study the existence of one-signed T-periodic solutions and sign-changing subharmonic solutions to the second order scalar ODEu′′ + f (t, u) = 0,being f : ℝ × ℝ → ℝ a continuous function T-periodic in the first variable and such that f (t, 0) ≡ 0. Partial extensions of the results to a general planar Hamiltonian systems are given, as well.

scholarly journals Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

2018 ◽  
Vol 1 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Mısır J. Mardanov ◽  
Yagub A. Sharifov ◽  
Kamala E. Ismayilova
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

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