Xiaoming He

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.

Multiple solutions for the Brezis-Nirenberg problem with a Hardy potential and singular coefficients

By energy estimates and by establishing a local (PS) condition, we establish the multiplicity of solutions to a class of semi-linear Brezis-Nirenberg type problems with a Hardy term and singular coefficients via the pseudo-index theory.

Nontrivial solitary waves to the generalized Kadomtsev-Petviashvili equations

Abstract In this note, we study the existence of nontrivial solitary waves for the generalized Kadomtsev–Petviashvili equation in multi-dimensional spaces. Our main tool is a recent linking theorem stated in a paper by Szulkin and Zou [A. Szulkin, W. Zou, Homoclinic orbit for asymptotically linear Hamiltonian systems, J. Funct. Anal. 187 (2001) 25–41].