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- W2097680722 abstract "We study the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mover accent=true><mml:mi>q</mml:mi><mml:mo>¨</mml:mo></mml:mover><mml:mo>−</mml:mo><mml:mi>L</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>q</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mo>∇</mml:mo><mml:mi>q</mml:mi></mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>L</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>is unnecessarily positive definite for all<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>t</mml:mi><mml:mo>∈</mml:mo><mml:mi>ℝ</mml:mi></mml:mrow></mml:math>, and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mo>∇</mml:mo><mml:mi>q</mml:mi></mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>is of at most linear growth and satisfies some twist condition between the origin and the infinity." @default.
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- W2097680722 date "2012-01-01" @default.
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- W2097680722 title "Homoclinic Orbits for Second-Order Hamiltonian Systems with Some Twist Condition" @default.
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- W2097680722 doi "https://doi.org/10.1155/2012/250607" @default.
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