scholarly journals On Homoclinic Solutions for First-Order Superquadratic Hamiltonian Systems with Spectrum Point Zero

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Feng Li ◽  
Juntao Sun
Keyword(s):  
Critical Point ◽  
Hamiltonian Systems ◽  
Homoclinic Solutions ◽  
Strongly Indefinite Functionals ◽  
Spectrum Point ◽  
First Order ◽  
Existence And Multiplicity ◽  
Critical Point Theorems

The existence and multiplicity of homoclinic solutions for a class of first-order periodic Hamiltonian systems with spectrum point zero are obtained. The proof is based on two critical point theorems for strongly indefinite functionals. Some recent results are improved and extended.

scholarly journals Homoclinic solutions of 2nth-order difference equations containing both advance and retardation

2016 ◽  
Vol 14 (1) ◽  
pp. 520-530 ◽  
Author(s):  
Yuhua Long ◽  
Yuanbiao Zhang ◽  
Haiping Shi
Keyword(s):  
Difference Equation ◽  
Critical Point ◽  
Difference Equations ◽  
Homoclinic Solutions ◽  
Mountain Pass ◽  
Nonlinear Difference Equation ◽  
Mountain Pass Lemma ◽  
Order Difference ◽  
Existence And Multiplicity ◽  
New Criteria

AbstractBy using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.

scholarly journals Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Xiaoping Wang
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Satisfying Condition ◽  
Sufficient Conditions ◽  
Homoclinic Solutions ◽  
First Order ◽  
Discrete Hamiltonian System

We give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian systemΔx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n)has no solution(x(n),y(n))satisfying condition0<∑n=-∞+∞[|x(n)|ν+(1+β(n))|y(n)|μ]<+∞, whereμ,ν>1and1/μ+1/ν=1andα(n),β(n),andγ(n)are real-valued functions defined onℤ.

Homoclinic Solutions for a Class of Hamiltonian Systems

2004 ◽  
Vol 4 (1) ◽  
Author(s):  
Morched Boughariou
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Homoclinic Solution ◽  
Homoclinic Solutions ◽  
Absolute Maximum ◽  
First Order ◽  
Order Hamiltonian System

AbstractWe consider the first order Hamiltonian systemq̇ = Hp(p, q),ṗ = −Hq(p, q), (HS)where p, q : ℝ → ℝUnder the condition that V has a unique absolute maximum at 0 and some technical assumptions on H, we prove that (HS) has a non-trivial homoclinic solution.

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