Abstract:

In this paper, we obtain existence and multiplicity of periodic solutions for 1-dimensional p-Laplacian equation $(|x'|^{p-2}x')'+f(t, x)=0$, where $f\in C(\mathbb{R} \times\mathbb{R} , \mathbb{R} )$ is \pi$-periodic in the first variable and satisfies the assumption $\frac{f(t, x)}{\mid x\mid^{p-2}x}\rightarrow 0$, as $\mid x\mid \rightarrow 0$. The new existence results can be applied to situations in which the more classical equation $x''+f(t, x)=0$. Proofs are based on Poincaré-Birkhoff twist theorem.

Key words: Hamiltonian systems, Periodic solution, Poincaré-Birkhoff twist theorem, Spiral property