Olimpio H. Miyagaki

Existence and concentration of solution for a class of fractional elliptic equation in \mathbb {R}^N via penalization method

In this paper, we study the existence and concentration of positive solution for the following class of fractional elliptic equation

CRITICAL AND SUBCRITICAL FRACTIONAL PROBLEMS WITH VANISHING POTENTIALS

begin{aligned} epsilon ^{2s} (-Delta )^{s}{u}+V(z)u=f(u) quad text{ in } ; mathbb {R}^{N}, end{aligned}

Radial solutions of inhomogeneous fourth order elliptic equations and weighted Sobolev embeddings

ϵ2s(-Δ)su+V(z)u=f(u)inRN,where

A sign-changing solution for an asymptotically linear Schrödinger equation

epsilon

Concentration phenomena for fractional elliptic equations involving exponential critical growth

ϵ is a positive parameter, f is a continuous function having a subcritical growth, V is a continuous potential possessing a local minimum,