Homoclinics for singular strong force Lagrangian systems
2019 ◽
Vol 9
(1)
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pp. 644-653
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Keyword(s):
Abstract We study the existence of homoclinic solutions for a class of Lagrangian systems $\begin{array}{} \frac{d}{dt} \end{array} $(∇Φ(u̇(t))) + ∇uV(t, u(t)) = 0, where t ∈ ℝ, Φ : ℝ2 → [0, ∞) is a G-function in the sense of Trudinger, V : ℝ × (ℝ2 ∖ {ξ}) → ℝ is a C1-smooth potential with a single well of infinite depth at a point ξ ∈ ℝ2 ∖ {0} and a unique strict global maximum 0 at the origin. Under a strong force condition around the singular point ξ, via minimization of an action integral, we will prove the existence of at least two geometrically distinct homoclinic solutions u± : ℝ → ℝ2 ∖ {ξ}.
2021 ◽
Vol 60
(2)
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Keyword(s):
2019 ◽
Vol 472
(1)
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pp. 352-371
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Keyword(s):
2003 ◽
Vol 18
(23)
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pp. 1591-1596
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Keyword(s):
2009 ◽
Vol 11
(02)
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pp. 309-335
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Keyword(s):
2006 ◽
Vol 317
(1)
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pp. 1-13
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2007 ◽
Vol 136
(04)
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pp. 1229-1236
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2018 ◽
Vol 33
(36)
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pp. 1850222
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