Abstract
We consider the following nonperiodic diffusion systems
where \({b\in C(\mathbb{R}\times\mathbb{R}^{N},\mathbb{R}^{N}), G\in C^{1} (\mathbb{R}\times\mathbb{R}^{N}\times\mathbb{R}^{2m},\mathbb{R})}\) and \({z:=(u,v): \mathbb{R}\times\mathbb{R}^{N}\rightarrow\mathbb{R}^{m}\times\mathbb{R}^{m}}\). Suppose that the potential V is positive constant and G(t, x, z) is superquadratic in z as |z| → ∞. By applying a generalized linking theorem for strongly indefinite functionals, we obtain homoclinic solutions z satisfying z(t, x) → 0 as |(t, x)| → ∞.
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This work was supported by the Natural Science Foundation of China and the Scientific Research Foundation of Graduate School of Southeast University(YBJJ0928).
An erratum to this article can be found at http://dx.doi.org/10.1007/s00030-010-0089-7
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Wang, J., Xu, J., Zhang, F. et al. Homoclinic orbits for an unbounded superquadratic. Nonlinear Differ. Equ. Appl. 17, 411–435 (2010). https://doi.org/10.1007/s00030-010-0060-7
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DOI: https://doi.org/10.1007/s00030-010-0060-7