Fukun Zhao

A note on superlinear Hamiltonian elliptic systems

This paper is concerned with the superlinear periodic elliptic systems of Hamiltonian type in the whole space. The existence of a ground state solution as well as an infinite number of geometrically distinct solutions is obtained.

Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems

We study the following nonperiodic Hamiltonian system , where is the form . We introduce a new assumption on and prove that the corresponding Hamiltonian operator has only point spectrum. Moreover, by applying a generalized linking theorem for strongly indefinite functionals, we establish the existence of homoclinic orbits for asymptotically quadratic nonlinearity as well as the existence of infinitely many homoclinic orbits for superquadratic nonlinearity.

Multiple solutions for asymptotically quadratic and superquadratic elliptic system of Hamiltonian type

This paper is concerned with the following nonperiodic Hamiltonian elliptic system { - Δ u + V ( x ) u = H v ( x , u , v ) x ? R N , - Δ v + V ( x ) v = H u ( x , u , v ) x ? R N , u ( x ) ? 0 , v ( x ) ? 0 as | x | ? ∞ , where z = ( u , v ) : R N ? R i? R , N ? 3, and the potential V(x) is nonperiodic and sign-changing. By applying a generalized linking theorem for strongly indefinite functionals, we establish the existence of multiple solutions for asymptotically quadratic nonlinearity as well as the existence of infinitely many solutions for superquadratic nonlinearity.

Infinitely many solutions to quasilinear elliptic equation with concave and convex terms

In this paper, we are concerned with the following quasilinear elliptic equation with concave and convex terms

Existence and multiplicity of periodic solution for non-autonomous second-order systems with linear nonlinearity☆

-\Delta u-{\frac12}u\Delta(|u|^2)=\alpha|u|^{p-2}u+\beta|u|^{q-2}u,\quad x\in \Omega, \leqno(\rom{P})

Multiple Solutions for Asymptotically Linear Elliptic Systems

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Multiple solutions for a superlinear and periodic elliptic system on {\mathbb{R}^N}

\Omega\subset\mathbb{R}^N

On Hamiltonian elliptic systems with periodic or non-periodic potentials

is a bounded smooth domain,