Interior Bubbling Solutions for an Elliptic Equation with Slightly Subcritical Nonlinearity

In this paper, we considered the Neumann elliptic equation (Pε): −Δu+K(x)u=u(n+2)/(n−2)−ε, u>0 in Ω, ∂u/∂ν=0 on ∂Ω, where Ω is a smooth bounded domain Rn, n≥6, ε small positive real and K function Ω¯. Using refined asymptotic estimates of gradient associated Euler–Lagrange functional, constructed simple non-simple interior bubbling solutions (Pε) which allowed us to prove multiplicity results for provided that small. The existence new phenomenon subcritical problems.