15 citations · 46 across the 36 of their papers we have counts for
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Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory
Marco G. Ghimenti, Anna Maria Micheletti
Given (M, g0) we consider the problem -ε^2Delta_{g0+h}u + u = (u+)^{p-1} with (ε, h) \in (0, ε0) \times Bρ. Here Bρ is a ball centered at 0 with radius ρ in the Banach space of all…
On the number of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds
Marco G. Ghimenti, Anna Maria Micheletti
We consider the problem -ε^2Δ_gu+u = |u|^{p-2}u in M, where (M,g) is a symmetric Riemannian manifold. We give a multiplicity result for antisymmetric changing sign solutions.
Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary
Marco G. Ghimenti, Anna Maria Micheletti
Let (M,g) be a smooth connected compact Riemannian manifold of finite dimension n \geq 2 with a smooth boundary \partial M. We consider the problem -ε^2Δ_gu+u=|u|^{p-2}u, u>0 on M,…
The Nonlinear Schroedinger Equation: Existence, Stability and Dynamics of Solitons
Vieri Benci, Marco G. Ghimenti, Anna Maria Micheletti
In this paper we present some recent results concerning the ex- istence, the stability and the dynamics of solitons occurring in the nonlinear Schroedinger equation when the parame…
On the Existence of the Fundamental Eigenvalue of an Elliptic Problem in R^N
Jacopo Bellazzini, Vieri Benci, Marco G. Ghimenti +1
We study an eigenvalue problem for functions in R^N and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of th…
Solutions for a Nonhomogeneous Nonlinear Schroedinger Equation with Double Power Nonlinearity
Marco G. Ghimenti, Anna Maria Micheletti
We consider the problem -Δu+V(x)u = f'(u)+g(x) in RN, under the assumption limx \rightarrow \infty V (x) = 0, and with the non linear term f with a double power behavior. We prove…