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Zbl 0999.34039
Tang, Chunlei; Wu, Xingping
Periodic solutions for second order systems with not uniformly coercive potential.
(English)
[J] J. Math. Anal. Appl. 259, No.2, 386-397 (2001). ISSN 0022-247X

The authors study the second-order system $$\ddot u(t)=\nabla F(t,u(t))\quad \text{a.e.}\quad t\in[0, T],\qquad u(0)-u(T)=\dot u(0)-\dot u(T)=0,$$ with locally coercive potential, that is $F(t,x)\rightarrow\infty$ a.e. for $t$ in some positive measure subset of $[0, T]$. Existence and multiplicity of periodic solutions are obtained. The result is established using an analogy of Egorov's theorem, properties of subadditive functions, the least action principle, and a three-critical-point theorem proposed by Brezis and Nirenberg.
[Ivan Ginchev (Varna)]
MSC 2000:
*34C25 Periodic solutions of ODE

Keywords: periodic solutions; second-order systems; subadditivity; coercivity; Sobolev's inequality; critical points

Cited in: Zbl 1096.34027

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