Yiwei Ye

Multiple solutions for Kirchhoff-type equations in RN

This paper is devoted to the existence of infinitely many solutions for a class of Kirchhoff-type equations setting on RN. Based on the minimax methods in critical point theory, we obtain infinitely many large-energy and small-energy solutions, which unify and sharply improve the recent results of Wu [“Existence of nontrivial solutions and high energy solutions for Schrodinger–Kirchhoff-type equations in RN,” Nonlinear Anal.: Real World Appl. 12, 1278–1287 (2011)].

Infinitely many periodic solutions of non-autonomous second-order Hamiltonian systems

In this paper, we study the existence of infinitely many periodic solutions for the non-autonomous second-order Hamiltonian systems with symmetry. Based on the minimax methods in critical point theory, in particular, the fountain theorem of Bartsch and the symmetric mountain pass lemma due to Kajikiya, we obtain the existence results for both the superquadratic case and the subquadratic case, which unify and sharply improve some recent results in the literature.

Periodic solutions for second-order discrete Hamiltonian system with a change of sign in potential

Some existence results of periodic solutions are obtained for nonautonomous second-order discrete Hamiltonian system with a change of sign in potential by the minimax methods in critical point theory.

Periodic solutions of second-order systems with subquadratic convex potential

In this paper, we investigate the existence of periodic solutions for the second order systems at resonance: { ü(t) + m2ω2u(t) +∇F(t, u(t)) = 0 a.e. t ∈ [0, T], u(0)− u(T) = u̇(0)− u̇(T) = 0, where m > 0, the potential F(t, x) is convex in x and satisfies some general subquadratic conditions. The main results generalize and improve Theorem 3.7 in J. Mawhin and M. Willem [Critical point theory and Hamiltonian systems, Springer-Verlag, New York, 1989].