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Zhang, Liang; Tang, X. H.

Periodic solutions for some nonautonomous \(p(t)\)-Laplacian hamiltonian systems. (English) Zbl 1274.34129

Appl. Math., Praha 58, No. 1, 39-61 (2013).
Summary: We deal with the existence of periodic solutions of the \(p(t)\)-Laplacian Hamiltonian system \[ \begin{cases} \frac {\text{d}}{\text{dt}}(| \dot {u}| ^{p(t)-2}\dot {u}(t))= \nabla F(t,u(t))\; \text{ a. e. }\; t\in [0, T],\\ u(0)-u(T)=\dot {u}(0)-\dot {u}(T)= 0. \end{cases} \] Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.

Cited in 2 Documents

MSC:

34C25 Periodic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences

Keywords:

periodic solution; Hamiltonian system; \(p(t)\)-Laplacian system; critical point; minimax principle; least action principle
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\textit{L. Zhang} and \textit{X. H. Tang}, Appl. Math., Praha 58, No. 1, 39--61 (2013; Zbl 1274.34129)
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