We study the existence, multiplicity and concentration behavior of positive solutions for the
nonlinear Kirchhoff type problem where ε> 0 is a parameter and a, b> 0 are constants; V is a …

In this paper we study the existence and concentration behaviors of positive solutions to the
Kirchhoff type equations-ε^ 2 M\left (ε^ 2-N\!\! R^ N| ∇ u|^ 2\, dx\right) Δ u\!+\! V (x) u\!=\! f …

We consider the semilinear equation ε 2 s (− Δ) s u+ V (x) u− up= 0, u> 0, u∈ H 2 s (RN)
where 0< s< 1, 1< p< N+ 2 s N− 2 s, V (x) is a sufficiently smooth potential with inf RV (x)> 0 …

STATIONARY STATES OF NONLINEAR DIRAC EQUATIONS WITH GENERAL POTENTIALS
Page 1 Reviews in Mathematical Physics Vol. 20, No. 8 (2008) 1007–1032 c World Scientific …

For elliptic equations ε 2 Δ u− V (x) u+ f (u)= 0, x∈ RN, N≧ 3, we develop a new variational
approach to construct localized positive solutions which concentrate at an isolated …

We consider a class of equations of the form-ε^ 2 Δ u+ V (x) u= f (u),\quad u ∈ H^ 1 (\bf R^
N). By variational methods, we show the existence of families of positive solutions …

We study the semiclassical limit for the following system of Maxwell--Schrödinger equations: -
ℏ^22mΔv+v+ωϕv-γv^p=0,\;\;-Δϕ=4πωv^2, where ℏ, m, ω, γ>0, v, ϕ:R^3→R, 1<p<117. This …

We consider the problem ε^ 2 Δ uV (x) u+ u^ p= 0,\;\;\;\;\; u> 0,\;\;\; u ∈ H^ 1 (\cal R^ 2), where
p> 1, ε> 0 is a small parameter, and V is a uniformly positive, smooth potential. Let Γ be a …

We consider the following nonlinear problem in $\R^ N $$$\label {eq}-\Delta u+ V (| y|) u=
u^{p},\quad u> 0 {in}\R^ N, u\in H^ 1 (\R^ N) $$ where $ V (r) $ is a positive function, $1< …

Recently, two-component systems of nonlinear Schrödinger equations with trap potentials
have been well-known to describe a binary mixture of Bose–Einstein condensates called a …