Abstract. We study Trudinger type inequalities in R N and their best exponents α N . We show for α ∈ (0, α N ), α N = Nω

We consider the existence of positive solutions of the following semilinear elliptic problem in R N :

We are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics. We convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity. We also investigate non-degeneracy of positive radial solution for converted semilinear elliptic equation.

No abstract

In this paper, we are concerned with the uniqueness and the nondegeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE analysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified Schrödinger equations.2010 Mathematics Subject Classification. 35J61, 35A02, 35B05.