Singular perturbation problems with turning points arise as mathematical models for various
physical phenomena. The problem with interior turning point represent one-dimensional …

We study the ground state which minimizes a Gross–Pitaevskii energy with general non-
radial trapping potential, under the unit mass constraint, in the Thomas–Fermi limit where a …

We consider the inhomogeneous Allen–Cahn equation ϵ^ 2 Δ u\,+\, V (y)(1-u^ 2)\, u\,=\,
0\quad in\Omega,\qquad ∂ u ∂ ν\,=\, 0\quad on\partial Ω, ϵ 2 Δ u+ V (y)(1-u 2) u= 0 in Ω,∂ …

For a singularly perturbed equation of inhomogeneous Allen-Cahn type with positive
potential function in high dimensional general domain, we prove the existence of solutions …

We consider the nonlinear problem of inhomogeneous Allen–Cahn equation ϵ 2 Δ u+ V (y)
u (1− u 2)= 0 in Ω,∂ u∂ ν= 0 on∂ Ω, where Ω is a bounded domain in R 2 with smooth …

We consider the nonlinear problem of anisotropic Fife-Greenlee equation ε2div (∇ a (y)
u)+(u− P (y))(1− u2)= 0 inΩ,∇ a (y) u· ν= 0 on∂ Ω, where Ω is a bounded domain in R2 with …

This paper concerns general singularly perturbed second order semilinear elliptic equations
on bounded domains $ Omega subset R^ n $ with nonlinear natural boundary conditions …

We consider the singular perturbation problem− ε2Δu+ (u− a (| x|))(u− b (| x|))= 0 in the unit
ball of RN, N⩾ 1, under Neumann boundary conditions. The assumption that a (r)− b (r) …

1− u 2)= 0 in Ω,∂ u∂ ν= 0 on∂ Ω, where Ω is a bounded domain in R2 with smooth
boundary,− 1< a (y)< 1, ε is a small parameter, ν denotes the outward normal of∂ Ω …

We discuss the existence and the Morse index of solutions to the problem Δ U+ λ e U= 0 in Ω
R, U= 0 on∂ Ω R, where Ω R is a tubular domain in the plane with fixed width. We obtain the …