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• W4285184535 abstract "<p style='text-indent:20px;'>Consider the following second-order perturbed Hamiltonian systems</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE1> begin{document}$ left{begin{array}{l}{ddot{u}(t)+nabla_u F(t,u)=nabla_{u}G(t,u),quad tin{bf{R}},} {u(0)-u(T)=dot{u}(0)-dot{u}(T)=bf0,quad T&gt;0,}end{array}right. $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id=M1>begin{document}$ F(t,u)=-K(t,u)+W(t,u) $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=M2>begin{document}$ K $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=M3>begin{document}$ W $end{document}</tex-math></inline-formula> are measurable and <inline-formula><tex-math id=M4>begin{document}$ T- $end{document}</tex-math></inline-formula>periodic in <inline-formula><tex-math id=M5>begin{document}$ t $end{document}</tex-math></inline-formula> for all <inline-formula><tex-math id=M6>begin{document}$ uinbf{R}^N $end{document}</tex-math></inline-formula>, continuously differentiable in <inline-formula><tex-math id=M7>begin{document}$ u $end{document}</tex-math></inline-formula> for a.e. <inline-formula><tex-math id=M8>begin{document}$ tin[0,T] $end{document}</tex-math></inline-formula> and even in <inline-formula><tex-math id=M9>begin{document}$ u $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=M10>begin{document}$ Gin C^1left(bf{R}timesbf{R}^N,bf{R}right) $end{document}</tex-math></inline-formula> is also <inline-formula><tex-math id=M11>begin{document}$ T- $end{document}</tex-math></inline-formula>periodic in <inline-formula><tex-math id=M12>begin{document}$ t $end{document}</tex-math></inline-formula>, but <inline-formula><tex-math id=M13>begin{document}$ G $end{document}</tex-math></inline-formula> maybe has no parity in <inline-formula><tex-math id=M14>begin{document}$ u $end{document}</tex-math></inline-formula>. Assume that <inline-formula><tex-math id=M15>begin{document}$ W $end{document}</tex-math></inline-formula> is local superquadratic and <inline-formula><tex-math id=M16>begin{document}$ G $end{document}</tex-math></inline-formula> is subquadratic at the infinity and <inline-formula><tex-math id=M17>begin{document}$ K $end{document}</tex-math></inline-formula> satisfies pinched condition, the existence of infinitely many weak periodic solutions for above perturbed systems is obtained via the Bolle's perturbation method, which generalizes and improves some previous results.</p>" @default.
• W4285184535 created "2022-07-14" @default.
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• W4285184535 date "2022-01-01" @default.
• W4285184535 modified "2023-10-09" @default.
• W4285184535 title "Multiplicity of periodic solutions for second-order perturbed Hamiltonian systems with local superquadratic conditions" @default.
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• W4285184535 doi "https://doi.org/10.3934/cpaa.2022098" @default.
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