Electron. J. Diff. Equ., Vol. 2013 (2013), No. 259, pp. 1-12.

Existence of solutions for fractional Hamiltonian systems

Cesar Torres

Abstract:
In this work we prove the existence of solutions for the fractional differential equation
$$ _{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u(t)) + L(t)u(t) = \nabla W(t,u(t)),\quad u\in H^{\alpha}(\mathbb{R}, \mathbb{R}^{N}). $$
where $\alpha \in (1/2, 1)$. Assuming L is coercive at infinity we show that this equation has at least one nontrivial solution.

Submitted June 10, 2013. Published November 26, 2013.
Math Subject Classifications: 26A33, 34C37, 35A15, 35B38.
Key Words: Liouville-Weyl fractional derivative; fractional Hamiltonian systems; critical point; variational methods.

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César Torres
Departamento de Ingeniería Matemática
and Centro de Modelamiento Matemático
UMR2071 CNRS-UChile, Universidad de Chile
Santiago, Chile
email: ctorres@dim.uchile.cl

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