Note on homoclinic solutions to nonautonomous Hamiltonian systems with sign-changing nonlinear part
DOI:
https://doi.org/10.12775/TMNA.2025.034Słowa kluczowe
Hamiltonian systems, generalized linking theorem, sign-changing nonlinearity, homoclinic solutionsAbstrakt
In the paper, we utilize the recent variational, abstract theorem to show the existence of homoclinic solutions to the Hamiltonian system $$ \dot{z} = J D_z H(z, t), \quad t \in \mathbb{R}, $$ where the Hamiltonian $H \colon \mathbb{R}^{2N} \times \mathbb{R}\rightarrow \mathbb{R}$ is of the form $$ H(z, t) = \frac12 Az \cdot z + \Gamma(t) ( F(z) - \lambda G(z)) $$ for some symmetric matrix $A$.Bibliografia
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