scholarly journals Existence and Nonexistence of Nontrivial Doubly Periodic Solutions of Nonlinear Telegraph Equations

2021 ◽  
pp. 70-80
Author(s):  
Nan Deng
Keyword(s):  
Periodic Solutions ◽  
Study Design ◽  
Point Theorem ◽  
Information Science ◽  
Telegraph Equation ◽  
Applied Science ◽  
Positive Parameter ◽  
Design Study ◽  
Existence And Nonexistence ◽  
Telegraph Equations

Aims/ Objectives: We discuss the existence and nonexistence of nontrivial nonnegative doubly periodic solutions for nonlinear telegraph equations                                                                  utt-uxx+cut+a(t,x)u=λf (t,x,u) , where c > 0 is a constant, λ > 0 is a positive parameter, a ∈ C(R2,R+), f ∈ C(R2 × R+,R+), and a, f are 2π-periodic in t and x. The proof is based on a known xed point theorem due to Schauder. In previous articles, a single telegraph equation or telegraph system have been widely studied, but there is relatively little research on nonlinear telegraph equations with a parameter and the nonlinearities are nonnegative. We would like do some research on this topic. We give new conclusions on the existence and nonexistence of nontrivial nonnegative doubly periodic solutions for nonlinear telegraph equations under sublinear assumptions. Study Design: Study on the existence and nonexistence of nontrivial nonnegative doubly periodic solutions. Place and Duration of Study: School of Applied Science, Beijing Information Science & Technology University, September 2020 to present.Methodology: We prove the existence and nonexistence of nontrivial nonnegative doubly periodic solutions by the results of Schauder's xed point theorem. Results: We give new conclusions of existence and nonexistence of nontrivial nonnegative doubly periodic solutions for the equations. Conclusion: We prove the existence and nonexistence of nontrivial nonnegative doubly periodic solutions for nonlinear telegraph equations                                                                 utt − uxx + cut + a(t, x)u = λf (t, x, u), and give new conclusions.

scholarly journals Existence of Positive Periodic Solutions for a Class ofn-Species Competition Systems with Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Peilian Guo ◽  
Yansheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
The Fixed Point Theorem

By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class ofn-species competition systems with impulses. Meanwhile, we point out that the conclusion of (Yan, 2009) is incorrect.

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 and Nontrivial Periodic Solutions for a Class of Rayleigh-Type Equation with Two Deviating Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Meiqiang Feng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Type Equation ◽  
Index Theorem ◽  
Rayleigh Equation ◽  
Deviating Arguments ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions

The Rayleigh equation with two deviating argumentsx′′(t)+f(x'(t))+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=e(t)is studied. By using Leray-Schauder index theorem and Leray-Schauder fixed point theorem, we obtain some new results on the existence of periodic solutions, especially for the existence of nontrivial periodic solutions to this equation. The results are illustrated with two examples, which cannot be handled using the existing results.

scholarly journals Two periodic solutions of neutral difference equations modelling physiological processes

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Difference Equations ◽  
Neutral Difference Equations ◽  
First Order ◽  
Analysis Techniques ◽  
Physiological Processes

We establish existence, multiplicity, and nonexistence of periodic solutions for a class of first-order neutral difference equations modelling physiological processes and conditions. Our approach is based on a fixed point theorem in cones as well as some analysis techniques.

scholarly journals Multiple Periodic Solutions for Discrete Nicholson’s Blowflies Type System

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui-Sheng Ding ◽  
Julio G. Dix
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Type System ◽  
Functional Difference ◽  
Difference System ◽  
Multiple Periodic Solutions

This paper is concerned with the existence of multiple periodic solutions for discrete Nicholson’s blowflies type system. By using the Leggett-Williams fixed point theorem, we obtain the existence of three nonnegative periodic solutions for discrete Nicholson’s blowflies type system. In order to show that, we first establish the existence of three nonnegative periodic solutions for then-dimensional functional difference systemyk+1=Akyk+fk, yk-τ, k∈ℤ, whereAkis not assumed to be diagonal as in some earlier results. In addition, a concrete example is also given to illustrate our results.

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.

Pengaruh Terapi Bekam Terhadap Kadar Kolesterol Pasien Hiperkolesterolemia Di Thibbun Nabawi Centre RSIA Zainab Pekanbaru Tahun 2019

2020 ◽  
Vol 10 (2) ◽  
pp. 1-12
Author(s):  
Isnaniar ◽  
Wiwik Norlita ◽  
Dikki Irma Wiradinata
Keyword(s):  
Study Design ◽  
Descriptive Study ◽  
P Value ◽  
Test Statistic ◽  
Design Study ◽  
Cross Sectional ◽  
Purposive Sampling ◽  
Experimental Cross ◽  
Effect Of Therapy

One of the treatment that is recommended by the Prophet Muhammad is to bekam . The research is aimed to effect of therapy of cupping to the levels of cholesterol  hypercholesterolemia in Tibbun Nabawi Center RSIA Zainab Pekanbaru with the design of the study . non- experimental cross sectional descriptive study, design This is a design study that the observations made are simultaneously at a time ( all the time). Samples of research this is 53 the respondents were drawn based on the criteria of inclusion using techniques nonprobality sampling the types of purposive sampling. Tools measure that is used is the data of patients whobruise in the year 2018. The analysis that is used is the analysis of univariate to determine the distribution of frequencies and bivariate using test Wilcoxon . Results of the study show from 53 people respondents who experienced hypercholesterolemia . as many as 14 people experienced adecrease. The results of the test statistic obtained results are significant with p value (0.000 ) < α (0.05),so it can be concluded that the cupping effect to decrease the levels of cholesterol in the blood in patients with hypercholesterolemia . It is expected that the community could use the therapy of cupping to overcome the diseasehypercholesterolemia . And can be concluded that the therapy cupping effect to decrease the levels of cholesterol in the blood in patients with hypercholesterolemia in Tibbun Nabawi Center.

Combined Parametrical and Transversal Excitation of a Stretched String in an Elastic Medium

2001 ◽  
Author(s):  
Caswita ◽  
A. H. P. van der Burgh
Keyword(s):  
Periodic Solutions ◽  
Elastic Medium ◽  
Integrodifferential Equation ◽  
Averaging Method ◽  
Telegraph Equation ◽  
Point Boundary ◽  
Time Periodic Solutions ◽  
The Stability ◽  
Two Parameters ◽  
Time Periodic

Abstract In this paper we consider a two-point boundary alue problem for an integrodifferential equation. This equation can be considered as a nonlinearly perturbed telegraph equation including both parametrical and transversal excitation. The attention will be focused on time-periodic solutions consisting of two modes. The first mode is generated by parametrical excitation and the second one is generated by vertical (transversal) excitation. This interaction of two modes can occur for special combinations of values of two parameters in the equation For the study of time-periodic solutions the averaging method will be used and the stability of the time-periodic solutions will be analyzed in linear approximation.

Heller Myotomy versus Heller Myotomy with Dor Fundoplication for Achalasia

2017 ◽  
Author(s):  
Jerald Borgella ◽  
Michael Choi ◽  
Miguel Burch
Keyword(s):  
Gastroesophageal Reflux ◽  
Study Design ◽  
Heller Myotomy ◽  
Clinical Case ◽  
Partial Fundoplication ◽  
Dor Fundoplication ◽  
Design Study ◽  
Study Intervention

This chapter provides a summary of the management of patients with achalasia and how the addition of a fundoplication can affect outcomes. The primary question asked is could the addition of a Dor fundoplication to a Heller myotomy decrease the incidence of pathologic gastroesophageal reflux? Starting with that question, it describes the basics of the study, including funding, year study began, year study was published, study location, who was studied, who was excluded, how many patients, study design, study intervention, follow-up, endpoints, results, and criticism and limitations. The chapter briefly reviews other relevant studies and information, discusses implications, and concludes with a relevant clinical case regarding treating a patient with either Heller myotomy or Heller myotomy plus partial fundoplication.

Gastroesophageal Junction Tumors Does Location Determine Treatment?

2017 ◽  
Author(s):  
Emily L. Siegel ◽  
Miguel Burch
Keyword(s):  
Study Design ◽  
Clinical Case ◽  
Classification Scheme ◽  
Treatment Approach ◽  
Gastroesophageal Junction ◽  
Design Study ◽  
Appropriate Treatment ◽  
Study Intervention ◽  
Landmark Study

This chapter summarizes a landmark study in treatment of gastroesophageal (GE) junction tumors. Should an anatomically based classification scheme of GE tumors define the appropriate treatment approach for these tumors? Starting with that question, it describes the basis of the study, including funding, year study began, year study was published, study location, who was studied, who was excluded, how many patients, study design, study intervention, follow-up, endpoints, results, and criticism and limitations. The chapter briefly reviews other relevant studies and information, gives a summary and discusses implications, and concludes with a relevant clinical case involving possible gastrectomy and esophagectomy.

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