Antonio Ambrosetti

Dual variational methods in critical point theory and applications

This paper contains some general existence theorems for critical points of a continuously differentiable functional I on a real Banach space. The strongest results are for the case in which I is even. Applications are given to partial differential and integral equations.

Multiple bound states for the Schroedinger-Poisson problem

In this paper, we study the problem \[ \left\{\begin{array}{@{}l} -\Delta u + u + V(x)u = u^p,\\[3pt] -\Delta V = \lambda u^2, \quad \displaystyle\lim_{|x| \to +\infty} V(x)=0, \end{array}\right. \] where u, V : ℝ3 → ℝ are radial functions, λ > 0 and 1 < p < 5. We give multiplicity results, depending on p and on the parameter λ.

Multiplicity results for some nonlinear Schrodinger equations with potentials

Abstract Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations with potentials are found by means of a perturbative variational method.

Multiplicity results for the Yamabe problem on Sn.

We discuss some results related to the existence of multiple solutions for the Yamabe problem.

Scalar curvature under boundary conditions

Abstract We discuss some existence results for the scalar curvature problems on manifolds with boundary. We address some perturbative cases using a finite-dimensional reduction, variational in nature.