In this paper we show that a radially symmetric superlinear Dirichlet problem in a ball has infinitely many solutions. This result is obtained even in cases of rapidly growing nonlinearities, that is, when the growth of the nonlinearity surpasses the critical exponent of the Sobolev embedding theorem. Our methods rely on the energy analysis and the phase-plane angle analysis of the solutions fo...

In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation −∆pu = |u| ∗ u + λf(x, u) in a smooth bounded domain Ω of R with homogeneous Dirichlet boundary conditions on ∂Ω, where p = Np/(N − p) is the critical Sobolev exponent and ∆pu = div(|∇u|∇u) is the p−laplacian. The proof is based on variational arguments and the classical con...

We show that positive solutions of a semilinear elliptic problem in the Sobolev critical exponent with Newmann conditions, related to conformal deformation of metrics inR+, are asymptotically symmetric in a neighborhood of the origin. As a consequence, we prove for a related problem of conformal deformation of metrics in R+ that if a solution satisfies a Kazdan-Warner-type identity, then the co...

We prove the existence of at least three weak solutions for the Dirichlet problem when the nonlinear term f is sublinear and p(x) is greater than n. This Dirichlet problem involves a general elliptic operator in divergence form (in particular, a p(x)-Laplace operator). Our method relies upon a recent critical point theorem obtained by Bonanno and Marano, and is combined with the theory of varia...

This paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais-Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the compactness in the Palais Smale condition and the order of the nonlinearity in the operator. The main result is applied to estimate the asyptotic behav...