Wenming Zou

Infinitely many homoclinic orbits for the second-order Hamiltonian systems

In this paper, the existence of homoclinic orbits for the second-order Hamiltonian systems without periodicity is studied and infinitely many homoclinic orbits for both superlinear and asymptotically linear cases are obtained.

Existence and concentration of ground states for Schrödinger-Poisson equations with critical growth

In this paper, we study the existence and concentration behavior of ground state solutions for a class of Schrodinger-Poisson equation with a parameter ɛ > 0. Under some suitable conditions on the nonlinearity f and the potential V, we prove that for e small, the equation has a ground state solution concentrating around global minimum of the potential V in the semi-classical limit. Also, the exponential decay of the ground state solutions is studied.

Infinitely many solutions for Hamiltonian systems

Abstract We consider two classes of the second-order Hamiltonian systems with symmetry. If the systems are asymptotically linear with resonance, we obtain infinitely many small-energy solutions by minimax technique. If the systems possess sign-changing potential, we also establish an existence theorem of infinitely many solutions by Morse theory.

A BERESTYCKI–LIONS THEOREM REVISITED

In 1983, Berestycki and Lions [Nonlinear scalar field equations I. Existence of a ground state, Arch. Ration. Mech. Anal.82 (1983) 313–346] studied the following elliptic problem: where N ≥ 3, g is subcritical at infinity. They proved the existence of a ground state under some appropriate growth restrictions on g. In the present paper, we improve this result by showing that under the critical growth assumption on g the problem admits a ground state. In addition we study a mountain pass characterization of the least energy solutions of the problem. Without the assumption of the monotonicity of the function , we show that the mountain pass value gives the least energy level.

Standing waves for nonlinear Schrödinger equations involving critical growth

We consider the following singularly perturbed nonlinear elliptic problem:

Existence and symmetry of positive ground states for a doubly critical Schrodinger system

-\e^2\Delta u+V(x)u=f(u),\ u\in H^1(\mathbb{R^N}),

Sign-changing Solutions and Phase Separation for an Elliptic System with Critical Exponent

where

New Linking Theorem and Sign-Changing Solutions

N\ge 3