In this paper we consider the problemFrom the characterization of the solutions of the linearized operator, we deduce the existence of nonradial solutions which bifurcate from the radial one when α is an even integer.

In this paper we study the problemwhere B1 is the unit ball of R 2 , f is a smooth nonlinearity and α, λ are real numbers with α > 0. From a careful study of the linearized operator we compute the Morse index of some radial solutions to (P). Moreover, using the bifurcation theory, we prove the existence of branches of nonradial solutions for suitable values of the positive parameter λ. The case f (λ, u) = λe u provides more detailed information.2 2 in (1.1), in many cases, can be merged into the equation.In the particular case of f (λ, s) = λe s problem (1.

We consider the Hénon problemwhere B 1 is the unit ball in R N and N 3. For ε > 0 small enough, we use α as a paramenter and prove the existence of a branch of nonradial solutions that bifurcates from the radial one when α is close to an even positive integer.

Abstract. In this paper we study the number of the boundary single peak solutions of the problemfor ε small and p subcritical. Under some suitable assumptions on the shape of the boundary near a critical point of the mean curvature, we are able to prove exact multiplicity results. Note that the degeneracy of the critical point is allowed.

The results of this study suggest that SD are an important problem in children with ADHD and may be linked to increased symptoms.