Multichain-type solutions for Hamiltonian systems.
Rabinowitz, Paul H., Coti Zelati, Vittorio (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Rabinowitz, Paul H., Coti Zelati, Vittorio (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Rabinowitz, Paul H. (1995)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Chen, Chao-Nien, Tzeng, Shyuh-yaur (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Joanna Janczewska, Jakub Maksymiuk (2012)
Open Mathematics
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We consider a conservative second order Hamiltonian system in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ 0 = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
Schechter, Martin (2006)
Boundary Value Problems [electronic only]
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Chen, Chao-Nien, Tzeng, Shyuh-yaur (1997)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Zevin, A.A. (1998)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Nkashama, M.N. (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Cid, Carlos, Yarur, Cecilia (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Marek Izydorek, Joanna Janczewska (2012)
Open Mathematics
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We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 {ζ→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits - the shadowing chain lemma - via minimization of action integrals and using simple geometrical arguments.
D. Arcoya (1989)
Extracta Mathematicae
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Schmitt, Klaus, Wang, Zhi-Qiang (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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