Abstract
We study periodic solutions of second order Hamiltonian systems with even potential. By making use of generalized Nehari manifold, some sufficient conditions are obtained to guarantee the multiplicity and minimality of periodic solutions for second order Hamiltonian systems. Our results generalize the outcome in the literature.
Highlights
Denote by N, Z, R∗, R the sets of all natural numbers, integers, nonnegative real numbers, and real numbers, respectively
We study periodic solutions of second order Hamiltonian systems with even potential
When A = 0, in his pioneering work [1] of 1978, Rabinowitz established the existence of periodic solutions of (1) when V satisfies (V1), (V2), and the well-known ARcondition: (V7)
Summary
Received 26 April 2014; Revised 21 July 2014; Accepted August 2014; Published October 2014. We study periodic solutions of second order Hamiltonian systems with even potential. By making use of generalized Nehari manifold, some sufficient conditions are obtained to guarantee the multiplicity and minimality of periodic solutions for second order Hamiltonian systems. Our results generalize the outcome in the literature
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