Abstract
We investigate multiple solutions for the Hamiltonian system with singular potential nonlinearity and periodic condition. We get a theorem which shows the existence of the nontrivial weak periodic solution for the Hamiltonian system with singular potential nonlinearity. We obtain this result by using the variational method, critical point theory for indefinite functional.
Highlights
Let D be an open subset in R n with a compact complement C = R n\D, n ≥
In this paper we investigate the number of solutions (p(t), q(t)) ∈ C ([, π], D) with singular potential nonlinearity and periodic condition p( ̇t) = –Gq t, p(t), q(t), q( ̇t) = Gp t, p(t), q(t), ( . )
In Section, we investigate the Fréchet differentiability of the associated functional I(z) and recall the critical point theorem for indefinite functional
Summary
Satisfies the following conditions: (G ) There exists R > such that sup G t, z(t) + gradz G t, z(t) R n | (t, z) ∈ [ , π ] × R n\BR < +∞. In Section , we investigate the Fréchet differentiability of the associated functional I(z) and recall the critical point theorem for indefinite functional. In Section , we show that the associated functional I(z) satisfies the geometrical assumptions of the critical point theorem for indefinite functional and prove Theorem .
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