Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems
Keyword(s):
We give several sufficient conditions under which the first-order nonlinear Hamiltonian systemx'(t)=α(t)x(t)+f(t,y(t)), y'(t)=-g(t,x(t))-α(t)y(t)has no solution(x(t),y(t))satisfying condition0<∫-∞+∞[|x(t)|ν+(1+β(t))|y(t)|μ]dt<+∞,whereμ,ν>1and(1/μ)+(1/ν)=1,0≤xf(t,x)≤β(t)|x|μ,xg(t,x)≤γ0(t)|x|ν,β(t),γ0(t)≥0, andα(t)are locally Lebesgue integrable real-valued functions defined onℝ.
2019 ◽
Vol 43
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pp. 1163-1182
2020 ◽
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pp. 2050126
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2018 ◽
Vol 28
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pp. 1850038
1995 ◽
Vol 189
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pp. 585-601
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2011 ◽
Vol 54
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pp. 2583-2596
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