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Damped vibration problems with sign-changing nonlinearities: infinitely many periodic solutions

We obtain infinitely many nontrivial periodic solutions for a class of damped vibration problems, where nonlinearities are superlinear at infinity and primitive functions of nonlinearities are allowed to be sign-changing. By using some weaker conditions, our results extend and improve some existing results in the literature. Besides, some examples are given to illuminate our...

Discrete Schrödinger equations in the nonperiodic and superlinear cases: homoclinic solutions

Using variational methods, we study the existence and multiplicity of homoclinic solutions for a class of discrete Schrödinger equations in infinite m-dimensional lattices with nonlinearities being superlinear at infinity. Our results generalize some existing results in the literature by using some weaker conditions.

Multiple solutions of discrete Schrödinger equations with growing potentials

Under some weaker conditions than elsewhere, we obtain infinitely many homoclinic solutions for a class of discrete Schrödinger equations in infinite m dimensional lattices with nonlinearities being superlinear at infinity by using variational methods. Our result extends some existing results in the literature. MSC: 35Q51, 35Q55, 39A12, 39A70.

Existence and multiplicity of positive solutions for p-Laplacian elliptic equations

We study a p-Laplacian elliptic equation with Hardy term and Hardy-Sobolev critical exponent, where the nonlinearity is ( p − 1 ) -sublinear near zero and ( p ∗ ( s ) − 1 ) -sublinear near infinity ( p ∗ ( s ) = p ( N − s ) N − p is the Hardy-Sobolev critical exponent). By using variational methods and some analysis techniques, we obtain the existence and multiplicity of positive...

Quasilinear elliptic equations with Hardy terms and Hardy-Sobolev critical exponents: nontrivial solutions

In this paper, we obtain one positive solution and two nontrivial solutions of a quasilinear elliptic equation with p-Laplacian, Hardy term and Hardy-Sobolev critical exponent by using variational methods and some analysis techniques. In particular, our results extend some existing ones. MSC: 35B33, 35J60.

Homoclinic orbits for second order Hamiltonian systems with asymptotically linear terms at infinity

Guanwei Chen 0 1 0 Statistics, Anyang Normal University 1 School of Mathematics In this paper, by using some different asymptotically linear conditions from those previously used in Hamiltonian

Ground state homoclinic orbits of superquadratic damped vibration systems

Guanwei Chen 0 Xiaoming Zhao 1 0 School of Mathematics and Statistics, Anyang Normal University , Anyang, Henan Province 455000 , P.R. China 1 Petrochina Pipeline Company , Langfang, Hebei Province

Ground state periodic solutions for Duffing equations with superlinear nonlinearities

Guanwei Chen Jian Wang In this paper, we study a general second order differential equation with superlinear nonlinearity. We obtain ground state and geometrically distinct periodic solutions of

Erratum to: Infinitely many solutions for resonant cooperative elliptic systems with sublinear or superlinear terms

Calc. Var. Calculus of Variations Guanwei Chen 0 Shiwang Ma 0 0 S. Ma School of Mathematical Sciences and LPMC, Nankai University , Tianjin 300071 , People's Republic of China in the proof of