Existence and multiplicity of periodic solutions to differential equations with attractive singularities

2021 ◽  
pp. 1-26
Author(s):  
José Godoy ◽  
Robert Hakl ◽  
Xingchen Yu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Topological Degree ◽  
A Priori ◽  
New Method ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Upper And Lower Functions

The existence and multiplicity of T-periodic solutions to a class of differential equations with attractive singularities at the origin are investigated in the paper. The approach is based on a new method of construction of strict upper and lower functions. The multiplicity results of Ambrosetti–Prodi type are established using a priori estimates and certain properties of topological degree.

scholarly journals Positive Solutions for Nonlinear Fractional Differential Equations with Boundary Conditions Involving Riemann-Stieltjes Integrals

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Integral Boundary ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

We consider the existence of positive solutions for a class of nonlinear integral boundary value problems for fractional differential equations. By using some fixed point theorems, the existence and multiplicity results of positive solutions are obtained. The results obtained in this paper improve and generalize some well-known results.

scholarly journals Existence and Multiplicity Results for Nonlinear Differential Equations Depending on a Parameter in Semipositone Case

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Hailong Zhu ◽  
Shengjun Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Multiplicity Results ◽  
Second Order Differential Equations ◽  
Existence And Multiplicity ◽  
Nonlinear Alternative ◽  
Krasnosel’Skii’S Fixed Point Theorem ◽  
Alternative Principle

The existence and multiplicity of solutions for second-order differential equations with a parameter are discussed in this paper. We are mainly concerned with the semipositone case. The analysis relies on the nonlinear alternative principle of Leray-Schauder and Krasnosel'skii's fixed point theorem in cones.

Existence and Multiplicity Results for Systems of First-Order Differential Equations via the Method of Solution-Regions

2018 ◽  
Vol 18 (3) ◽  
pp. 469-485 ◽  
Author(s):  
Marlène Frigon
Keyword(s):  
Differential Equations ◽  
Upper And Lower Solutions ◽  
Multiplicity Results ◽  
First Order ◽  
Existence And Multiplicity ◽  
Method Of Solution ◽  
First Order Differential Equations

AbstractIn this paper, we establish existence and multiplicity results for systems of first-order differential equations. To this end, we introduce the method of solution-regions. It generalizes the method of upper and lower solutions and the method of solution-tubes. Our results can also be seen as viability results since we obtain solutions remaining in suitable regions. We give conditions insuring the existence of at least three viable solutions of a system of first-order differential equations. Many examples are presented to show that a large variety of sets can be solution-regions.

Degree, quaternions and periodic solutions

2021 ◽  
Vol 379 (2191) ◽  
pp. 20190378
Author(s):  
Jean Mawhin
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Topological Degree ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Brouwer Degree ◽  
Homogeneous Polynomials ◽  
Theme Issue ◽  
Existence And Multiplicity

The paper computes the Brouwer degree of some classes of homogeneous polynomials defined on quaternions and applies the results, together with a continuation theorem of coincidence degree theory, to the existence and multiplicity of periodic solutions of a class of systems of quaternionic valued ordinary differential equations. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

scholarly journals Periodic solutions of nonlinear vibrating beams

2003 ◽  
Vol 2003 (14) ◽  
pp. 823-841
Author(s):  
J. Berkovits ◽  
H. Leinfelder ◽  
V. Mustonen
Keyword(s):  
Multiple Solutions ◽  
A Priori ◽  
Linear Part ◽  
Invariant Subspaces ◽  
Beam Equation ◽  
External Forcing ◽  
Periodic Forcing ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Vibrating Beams

The aim of this paper is to prove new existence and multiplicity results for periodic semilinear beam equation with a nonlinear time-independent perturbation in case the period is not prescribed. Since the spectrum of the linear part varies with the period, the solvability of the equation depends crucially on the period which can be chosen as a free parameter. Since the period of the external forcing is generally unknown a priori, we consider the following natural problem. For a given time-independent nonlinearity, find periodsTfor which the equation is solvable for anyT-periodic forcing. We will also deal with the existence of multiple solutions when the nonlinearity interacts with the spectrum of the linear part. We show that under certain conditions multiple solutions do exist for any small forcing term with suitable periodT. The results are obtained via generalized Leray-Schauder degree and reductions to invariant subspaces.

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