GROUND STATE SOLUTION FOR A CLASS FRACTIONAL HAMILTONIAN SYSTEMS
Copyright policy )GROUND STATE SOLUTION FOR A CLASS FRACTIONAL HAMILTONIAN SYSTEMS
Summary: In this paper, we consider a class of Hamiltonian systems of the form \(_tD_\infty^\alpha(_{-\infty} D_t^\alpha u(t))+L(t) u(t)-\nabla W(t,u(t))=0\) where \(\alpha\in(\frac{1}{2},1)\), \(_{-\infty}D_t^\alpha\) and \(_tD_\infty^\alpha\) are left and right Liouville-Weyl fractional derivatives of order \(\alpha\) on the whole axis \(R\) respectively. Under weaker superquadratic conditions on the nonlinearity and asymptotically periodic assumptions, ground state solution is obtained by mainly using Local Mountain Pass Theorem, Concentration-Compactness Principle and a new form of Lions Lemma respect to fractional differential equations.
Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods, fractional Hamiltonian systems, ground state, local mountain pass theorem, concentration-compactness principle, Fractional ordinary differential equations, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces
Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods, fractional Hamiltonian systems, ground state, local mountain pass theorem, concentration-compactness principle, Fractional ordinary differential equations, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces
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