scholarly journals Existence and multiplicity of solutions for fractional Hamiltonian systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Guoqing Chai ◽  
Weiming Liu
Keyword(s):  
Hamiltonian Systems ◽  
Multiplicity Of Solutions ◽  
Fractional Hamiltonian Systems ◽  
Existence And Multiplicity

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.

scholarly journals Multiple Solutions for Generalized Asymptotical Linear Hamiltonian Systems Satisfying Bolza Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yuan Shan ◽  
Baoqing Liu
Keyword(s):  
Boundary Conditions ◽  
Hamiltonian Systems ◽  
Multiple Solutions ◽  
Index Theory ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Linear Hamiltonian Systems ◽  
Symmetric Mountain Pass Lemma

This paper is devoted to multiple solutions of generalized asymptotical linear Hamiltonian systems satisfying Bolza boundary conditions. We classify the linear Hamiltonian systems by the index theory and obtain the existence and multiplicity of solutions for the Hamiltonian systems, based on an application of the classical symmetric mountain pass lemma.

scholarly journals Existence and multiplicity of solutions for a fractional p-Laplacian equation with perturbation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhen Zhi ◽  
Lijun Yan ◽  
Zuodong Yang
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Analytical Techniques ◽  
Nontrivial Solutions ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity

AbstractIn this paper, we consider the existence of nontrivial solutions for a fractional p-Laplacian equation in a bounded domain. Under different assumptions of nonlinearities, we give existence and multiplicity results respectively. Our approach is based on variational methods and some analytical techniques.

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