arXiv subjects
Publications and source records attributed to Benedetta Pellacci.
The existence of a positive solution for a class of asymptotically lin- ear problems in exterior domains is established via a linking argument on the Nehari manifold and by means of a barycenter function.
We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect. We investigate the existence of nontrivial nonnegative solutions concentrating around local minima of both the potential and of the saturation function. Necessary conditions to locate the possible concentration points are also given.
Motivated by experimental studies on the anomalous diffusion of biological populations, we introduce a nonlocal differential operator which can be interpreted as the spectral square root of the Laplacian in bounded domains with Neumann homogeneous boundary conditions. Moreover, we study related linear and nonlinear problems exploiting a local realization of such operator as performed in [X. Cabre' and J. Tan. Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv. Math. 2010] for Dirichlet homogeneous data. In particular we tackle a class of nonautonomous nonlinearities of logistic type, proving some existence and uniqueness results for positive solutions by means of variational methods and bifurcation theory.
We obtain the existence of mountain pass solutions for quasi-linear equations without the typical assumptions which guarantee the boundedness of an arbitrary Palais-Smale sequence. This is done through a recent version of the monotonicity trick proved by the second author. The main results are new also for the p-Laplacian operator.
Orbital stability property for weakly coupled nonlinear Schrödinger equations is investigated. Different families of orbitally stable standing waves solutions will be found, generated by different classes of solutions of the associated elliptic problem. In particular, orbitally stable standing waves can be generated by least action solutions, but also by solutions with one trivial component whether or not they are ground states. Moreover, standing waves with components propagating with the same frequencies are orbitally stable if generated by vector solutions of a suitable single Schrödinger weakly coupled system, even if they are not ground states.
The soliton dynamics in the semiclassical limit for a weakly coupled nonlinear focusing Schrödinger systems in presence of a nonconstant potential is studied by taking as initial data some rescaled ground state solutions of an associate elliptic system.
We study the spectral structure of the complex linearized operator for a class of nonlinear Schrödinger systems, obtaining as byproduct some interesting properties of non-degenerate ground state of the associated elliptic system, such as being isolated and orbitally stable.
We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.
In this paper we prove existence and multiplicity results of unbounded critical points for a general class of weakly lower semicontinuous functionals. We will apply a suitable nonsmooth critical point theory.