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Homoclinic orbits for second order Hamiltonian system with quadratic growth

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Abstract

Some existence and multiplicity of homoclinic orbit for second order Hamiltonian system ẍ −a(t)x+W x (t,x)=0 are given by means of variational methods, where the potentialV(t,x)=−1/2a(t)|s|2+W(t,s) is quadratic ins at infinity and subquadratic ins at zero, and the functiona(t) satisfies the growth condition lim t→∞ ∫ t+l t a(t)dt=+∞, ∀l εr 1.

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Authors and Affiliations

  1. Department of Applied Mathematics, Zhejiang University, 310027, Hangzhou

    Wu Shaoping & Liu Jiaquan

  2. Department of Mathematics, Peking University, 100871, Beijing

    Wu Shaoping & Liu Jiaquan

Authors
  1. Wu Shaoping
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  2. Liu Jiaquan
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This work is partially supported by the National Natural Science Foundation of China and by the Zhejiang Natural Science Foundation.

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Wu, S., Liu, J. Homoclinic orbits for second order Hamiltonian system with quadratic growth. Appl. Math. 10, 399–410 (1995). https://doi.org/10.1007/BF02662495

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  • DOI: https://doi.org/10.1007/BF02662495

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