20 citations · 82 across the 16 of their papers we have counts for
16 papers
Compact embeddings for weighted fractional Sobolev spaces and applications to Nonlinear Schrödinger Equations
Federico Bernini, Sergio Rolando, Simone Secchi
The aim of this work is to prove a compact embedding for a weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the exist…
A note on quasilinear Schrödinger equations with singular or vanishing radial potentials
Marino Badiale, Michela Guida, Sergio Rolando
In this note we complete a previous study, where we got existence results for the quasilinear elliptic equation \begin{equation*} -Δw+ V\left( \left| x\right| \right) w - w \left(…
Existence results for a class of quasilinear Schrödinger equations with singular or vanishing potentials
Marino Badiale, Michela Guida, Sergio Rolando
Given two continuous functions and (), which may be singular or vanishing at zero as well as at infinity, we study the quasilinea…
Radial quasilinear elliptic problems with singular or vanishing potentials
Marino Badiale, Michela Guida, Sergio Rolando
In this paper we continue the work that we began in arXiv:1912.07537. Given , two measurable functions and , and a continuous fu…
Compactness and existence results for quasilinear elliptic problems with singular or vanishing potentials
Marino Badiale, Michela Guida, Sergio Rolando
Given , , two measurable functions , and a continuous function (), we study the quasilinear elliptic equ…
Multiple nonradial solutions for a nonlinear elliptic radial problem: an improved result
Sergio Rolando
We obtain an improved version of a recent result concerning the existence of nonnegative nonradial solutions $u\in D^{1,2}(\mathbb{R}^{N})\cap L^{2}(\mathbb{R}^{N},\left| x\right|…
Radial solutions for the bilaplacian equation with vanishing or singular radial potentials
Marino Badiale, Stefano Greco, Sergio Rolando
Given three measurable functions , and , , we consider the bilaplacian equation \[ Δ^2 u+V(|x|)u=K(|x|)f(u…
Multiple nonradial solutions for a nonlinear elliptic problem with singular and decaying radial potential
Sergio Rolando
Many existence and nonexistence results are known for nonnegative radial solutions to the equation \…
Standing waves for the NLS on the double-bridge graph and a rational-irrational dichotomy
Diego Noja, Sergio Rolando, Simone Secchi
We study a boundary value problem related to the search of standing waves for the nonlinear Schrödinger equation (NLS) on graphs. Precisely we are interested in characterizing the…
Compactness and existence results for the -Laplace equation
Marino Badiale, Michela Guida, Sergio Rolando
Given and two measurable functions and , , we define the weighted spaces \[ W=\left\{ u\in D^{1,p}(\mathbb{R}^{N}):\int_…
Compactness results for the -Laplace equation
Marino Badiale, Michela Guida, Sergio Rolando
Given and two measurable functions and , , we define the weighted spaces \[ W=\left\{ u\in D^{1,p}(\mathbb{R}^N):\int_{\mathbb{R}^N}V\left(\left|x…
Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence
Marino Badiale, Michela Guida, Sergio Rolando
We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation \[ -\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right|…
Nonlinear Schrödinger equations without compatibility conditions on the potentials
Michela Guida, Sergio Rolando
We study the existence of nonnegative solutions (and ground states) to the nonlinear Schrödinger equation in with radial potentials and super-linear or sub-linear no…
Some abstract results on the existence of bounded Palais-Smale sequences
Michela Guida, Sergio Rolando
Without compactness assumptions, we prove some abstract results which show that a functional on a Banach space admits bounded Palais-Smale s…
Compactness and existence results in weighted Sobolev spaces of radial functions, Part I: Compactness
Marino Badiale, Michela Guida, Sergio Rolando
Given two measurable functions and , , we define the weighted spaces \[ H_V^1 = \{u \in D^{1,2}(\mathbb{R}^N): \int_{\mathbb{R}^N}V(|x|)u^{2}dx < \infty…
A nonexistence result for a nonlinear elliptic equation with singular and decaying potential
Marino Badiale, Michela Guida, Sergio Rolando
The paper deals with positive radial solutions to a nonlinear elliptic equation with singular and decaying potential, for which several existence and nonexistence results are known…