scholarly journals Existence and multiplicity results of homoclinic solutions for fractional Hamiltonian systems

2017 ◽  
Vol 73 (6) ◽  
pp. 1325-1345 ◽  
Author(s):  
Yong Zhou ◽  
Lu Zhang
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Solutions ◽  
Multiplicity Results ◽  
Fractional Hamiltonian Systems ◽  
Existence And Multiplicity

scholarly journals Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Defang Ma ◽  
Zhan Zhou
Keyword(s):  
Difference Equations ◽  
Mountain Pass Theorem ◽  
Sufficient Conditions ◽  
Homoclinic Solutions ◽  
Fountain Theorem ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Special Cases ◽  
Discrete Nonlinear Schrödinger Equations ◽  
The Difference

A class of difference equations which include discrete nonlinear Schrödinger equations as special cases are considered. New sufficient conditions of the existence and multiplicity results of homoclinic solutions for the difference equations are obtained by making use of the mountain pass theorem and the fountain theorem, respectively. Recent results in the literature are generalized and greatly improved.

scholarly journals Some multiplicity results of homoclinic solutions for second order Hamiltonian systems

2020 ◽  
Vol 40 (1) ◽  
pp. 21-36
Author(s):  
Sara Barile ◽  
Addolorata Salvatore
Keyword(s):  
Hamiltonian Systems ◽  
Second Order ◽  
Homoclinic Solutions ◽  
Infinitely Many Solutions ◽  
Three Solutions ◽  
Multiplicity Results ◽  
Variational Techniques ◽  
Second Order Hamiltonian Systems ◽  
Bounded Functions ◽  
Fibering Method

We look for homoclinic solutions \(q:\mathbb{R} \rightarrow \mathbb{R}^N\) to the class of second order Hamiltonian systems \[-\ddot{q} + L(t)q = a(t) \nabla G_1(q) - b(t) \nabla G_2(q) + f(t) \quad t \in \mathbb{R}\] where \(L: \mathbb{R}\rightarrow \mathbb{R}^{N \times N}\) and \(a,b: \mathbb{R}\rightarrow \mathbb{R}\) are positive bounded functions, \(G_1, G_2: \mathbb{R}^N \rightarrow \mathbb{R}\) are positive homogeneous functions and \(f:\mathbb{R}\rightarrow\mathbb{R}^N\). Using variational techniques and the Pohozaev fibering method, we prove the existence of infinitely many solutions if \(f\equiv 0\) and the existence of at least three solutions if \(f\) is not trivial but small enough.

scholarly journals Multiplicity of Homoclinic Solutions for Fractional Hamiltonian Systems with Subquadratic Potential

Entropy ◽  
2017 ◽  
Vol 19 (2) ◽  
pp. 50 ◽  
Author(s):  
Neamat Nyamoradi ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Yong Zhou
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Solutions ◽  
Fractional Hamiltonian Systems

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.

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