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

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.

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
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