scholarly journals Multiplicity of Solutions for Fractional Hamiltonian Systems under Local Conditions

2020 ◽  
Vol 08 (08) ◽  
pp. 1472-1486
Author(s):  
Lili Wan
Keyword(s):  
Hamiltonian Systems ◽  
Local Conditions ◽  
Multiplicity Of Solutions ◽  
Fractional Hamiltonian Systems

Multiplicity of Solutions for Fractional Hamiltonian Systems with Liouville-Weyl Fractional Derivatives

2015 ◽  
Vol 18 (4) ◽  
Author(s):  
G. Amado Mendez Cruz ◽  
César E. Torres Ledesma
Keyword(s):  
Critical Theory ◽  
Hamiltonian Systems ◽  
Fractional Derivatives ◽  
Infinitely Many Solutions ◽  
Multiplicity Of Solutions ◽  
Fractional Hamiltonian Systems

AbstractIn this paper, we investigate the existence of infinitely many solutions for the following fractional Hamiltonian systems:tDu ∈ Hwhere α ∈ (1/2, 1), t ∈ ℝ, u ∈ ℝm({t ∈ (y − rare satisfied and W is of subquadratic growth as |u| → +∞, we show that (0.1) possesses infinitely many solutions via the genus properties in the critical theory. Recent results in Z. Zhang and R. Yuan [24] are significantly improved.

Multiplicity of Solutions for a Class of Perturbed Fractional Hamiltonian Systems

2020 ◽  
Vol 43 (6) ◽  
pp. 3897-3922
Author(s):  
César Torres ◽  
Oliverio Pichardo
Keyword(s):  
Hamiltonian Systems ◽  
Multiplicity Of Solutions ◽  
Fractional Hamiltonian Systems

Multiplicity of solutions to fractional Hamiltonian systems with impulsive effects

2017 ◽  
Vol 102 ◽  
pp. 254-263 ◽  
Author(s):  
Nemat Nyamoradi ◽  
Rosana Rodríguez-López
Keyword(s):  
Hamiltonian Systems ◽  
Impulsive Effects ◽  
Multiplicity Of Solutions ◽  
Fractional Hamiltonian Systems

Variational Approach to Homoclinic Solutions for Fractional Hamiltonian Systems

2017 ◽  
Vol 174 (1) ◽  
pp. 223-237
Author(s):  
Nemat Nyamoradi ◽  
Yong Zhou ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi
Keyword(s):  
Hamiltonian Systems ◽  
Variational Approach ◽  
Homoclinic Solutions ◽  
Fractional Hamiltonian Systems

Fractional Hamiltonian Systems with Locally Defined Potentials

2018 ◽  
Vol 195 (1) ◽  
pp. 563-571 ◽  
Author(s):  
A. Benhassine
Keyword(s):  
Hamiltonian Systems ◽  
Fractional Hamiltonian Systems

Ground state solutions for a class of fractional Hamiltonian systems

2019 ◽  
Vol 68 (2) ◽  
pp. 727-743
Author(s):  
Abderrazek Benhassine
Keyword(s):  
Hamiltonian Systems ◽  
Ground State ◽  
Ground State Solutions ◽  
Fractional Hamiltonian Systems

Infinitely-many solutions for subquadratic fractional Hamiltonian systems with potential changing sign

2015 ◽  
Vol 4 (1) ◽  
pp. 59-72 ◽  
Author(s):  
Ziheng Zhang ◽  
Rong Yuan
Keyword(s):  
Hamiltonian Systems ◽  
Mountain Pass Theorem ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Mountain Pass ◽  
Infinitely Many Solutions ◽  
Fractional Hamiltonian Systems ◽  
Symmetric Mountain Pass Theorem

AbstractIn this paper we are concerned with the existence of infinitely-many solutions for fractional Hamiltonian systems of the form ${\,}_tD^{\alpha }_{\infty }(_{-\infty }D^{\alpha }_{t}u(t))+L(t)u(t)=\nabla W(t,u(t))$, where ${\alpha \in (\frac{1}{2},1)}$, ${t\in \mathbb {R}}$, ${u\in \mathbb {R}^n}$, ${L\in C(\mathbb {R},\mathbb {R}^{n^2})}$ is a symmetric and positive definite matrix for all ${t\in \mathbb {R}}$, ${W\in C^1(\mathbb {R}\times \mathbb {R}^n,\mathbb {R})}$ and ${\nabla W(t,u)}$ is the gradient of ${W(t,u)}$ at u. The novelty of this paper is that, assuming L(t) is bounded in the sense that there are constants ${0<\tau _1<\tau _2< \infty }$ such that ${\tau _1 |u|^2\le (L(t)u,u)\le \tau _2 |u|^2}$ for all ${(t,u)\in \mathbb {R}\times \mathbb {R}^n}$ and ${W(t,u)}$ is of the form ${({a(t)}/({p+1}))|u|^{p+1}}$ such that ${a\in L^{\infty }(\mathbb {R},\mathbb {R})}$ can change its sign and ${0<p<1}$ is a constant, we show that the above fractional Hamiltonian systems possess infinitely-many solutions. The proof is based on the symmetric mountain pass theorem. Recent results in the literature are generalized and significantly improved.

Solutions for subquadratic fractional Hamiltonian systems without coercive conditions

2014 ◽  
Vol 37 (18) ◽  
pp. 2934-2945 ◽  
Author(s):  
Ziheng Zhang ◽  
Rong Yuan
Keyword(s):  
Hamiltonian Systems ◽  
Fractional Hamiltonian Systems
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