We consider nonlinear elliptic equations with small diffusion and Dirichlet boundary conditions. We construct changing sign solutions with peaks close to the boundary and consider the location of theâ€¦ (More)

where V (y) is a smooth bounded function with positive lower bound, Îµ > 0 is a small number, 2 < p < 2N/(N âˆ’2) if N > 2 and 2 < p < +âˆž if N = 2. Many works have been done on problem (1.1) recentlyâ€¦ (More)

We consider the following nonlinear field equation with super critical growth: (*) âˆ’âˆ†u + Î»u = Q(y)u N +2 N âˆ’2 , u > 0 in R N +m , u(y) â†’ 0 as |y| â†’ +âˆž, where m â‰¥ 1, Î» â‰¥ 0 and Q(y) is a boundedâ€¦ (More)

We obtain a local uniqueness result for bubbling solutions of the prescribed scalar curvature problem in R . Such result implies that some bubbling solutions preserve the symmetry from the scalarâ€¦ (More)

This is the first part of our comprehensive study on the structure of doubly periodic solutions for the Chern-Simons-Higgs equation with a small coupling constant. We first classify the bubbling typeâ€¦ (More)