Chun-Lei Tang

Multiple periodic solutions for superquadratic second-order discrete Hamiltonian systems☆

Abstract Some multiplicity results are obtained for periodic solutions of the nonautonomous superquadratic second-order discrete Hamiltonian systems Δ 2 u ( t - 1 ) + ∇ F ( t , u ( t ) ) = 0 ∀ t ∈ Z by using critical point theory, especially, a three critical points theorem proposed by Brezis and Nirenberg.

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)].

A uniqueness result for Kirchhoff type problems with singularity

Abstract In this work, by using the minimax method and some analysis techniques, we obtain the uniqueness of positive solutions for a class of Kirchhoff type problems with singularity.

Periodic solutions for a class of new superquadratic second order Hamiltonian systems

Abstract A new superquadratic growth condition is introduced, which is an extension of the well-known superquadratic growth condition due to P.H. Rabinowitz and the nonquadratic growth condition due to Gui-Hua Fei. An existence theorem is obtained for periodic solutions of a class of new superquadratic second order Hamiltonian systems by the minimax methods in critical point theory, specially, a local linking theorem.

Some existence results on periodic solutions of nonautonomous second-order differential systems with (q,p)-Laplacian

Abstract Some existence theorems are obtained for periodic solutions of nonautonomous second-order differential systems with ( q , p ) -Laplacian by using the least action principle and the minimax methods.

A positive ground state solution for a class of asymptotically periodic Schrödinger equations

In this paper, by using the reformative conditions, a class of asymptotically periodic Schrodinger equations are studied. Via the variational method, a positive ground state solution is obtained.

Multiple periodic solutions for second-order discrete Hamiltonian systems

Some existence and multiplicity results are obtained for periodic solutions of nonautonomous second-order discrete Hamiltonian systems with partially periodic potentials by using critical point theory.

Multiple positive solutions to a Kirchhoff type problem involving a critical nonlinearity

Abstract In this paper, we investigate a class of Kirchhoff type problem involving a critical nonlinearity − ( 1 + b ∫ Ω | ∇ u | 2 d x ) △ u = λ u + | u | 4 u , u ∈ H 0 1 ( Ω ) , where b > 0 , λ > λ 1 , λ 1 is the principal eigenvalue of ( − △ , H 0 1 ( Ω ) ) . With the help of the Nehari manifold, we obtain the multiplicity of positive solutions for λ in a small right neighborhood of λ 1 and prove that one of the solutions is a positive ground state solution, which is different from the result of Brezis–Nirenberg in 1983. This paper can be regarded as the complementary work of Naimen (2015).

Infinitely many periodic solutions for ordinary p-Laplacian systems

Abstract Some existence theorems are obtained for infinitely many periodic solutions of ordinary p-Laplacian systems by minimax methods in critical point theory.

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.