Existence and multiplicity results for periodic solutions of nonlinear difference equations

2006 ◽  
Vol 12 (7) ◽  
pp. 677-695 ◽  
Author(s):  
C. Bereanu ◽  
J. Mawhin
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Nonlinear Difference Equations ◽  
Multiplicity Results ◽  
Existence And Multiplicity

scholarly journals Infinitely Many Homoclinic Solutions for Second Order Nonlinear Difference Equations withp-Laplacian

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guowei Sun ◽  
Ali Mai
Keyword(s):  
Difference Equations ◽  
Critical Point Theory ◽  
Point Theory ◽  
Nehari Manifold ◽  
Homoclinic Solutions ◽  
Nonlinear Difference Equations ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Superlinear Nonlinearity ◽  
Laplacian Equations

We employ Nehari manifold methods and critical point theory to study the existence of nontrivial homoclinic solutions of discretep-Laplacian equations with a coercive weight function and superlinear nonlinearity. Without assuming the classical Ambrosetti-Rabinowitz condition and without any periodicity assumptions, we prove the existence and multiplicity results of the equations.

scholarly journals Positive Solutions of Nonlocal Boundary Value Problem for High-Order Nonlinear Fractional -Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Changlong Yu ◽  
Jufang Wang
Keyword(s):  
Positive Solutions ◽  
Difference Equations ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Nonlinear Difference Equations ◽  
Liouville Type ◽  
Fractional Difference ◽  
Multiplicity Results ◽  
Existence And Multiplicity

We study the nonlinear -difference equations of fractional order , , , , , where is the fractional -derivative of the Riemann-Liouville type of order , , , , and . We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems. Finally, we give examples to illustrate the results.

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’.

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