23 citations · 232 across the 109 of their papers we have counts for
128 papers · 1 filter
On nodal solutions with a prescribed number of nodes for a Kirchhoff-type problem
Haining Fan, Marco Squassina, Jianjun Zhang
We are concerned with the existence and asymptotic behavior of multiple radial sign-changing solutions with the nodal characterization for a Kirchhoff-type problem involving the no…
Generalized Chern-Simons-Schrodinger system with critical exponential growth: the zero mass case
Liejun Shen, Marco Squassina
We consider the existence of ground state solutions for a class of zero-mass Chern-Simons-Schrödinger systems \[ \left\{ \begin{array}{ll} \displaystyle -Δu +A_0 u+\sum\limits_{j=1…
Existence and concentration of normalized solutions for -Laplacian equations with logarithmic nonlinearity
Liejun Shen, Marco Squassina
We investigate the existence and concentration of normalized solutions for a -Laplacian problem with logarithmic nonlinearity of type \[ \left\{ \begin{array}{ll} \displaystyle…
Normalized solutions of quasilinear Schrödinger equations with a general nonlinearity
Ting Deng, Marco Squassina, Jianjun Zhang +1
We are concerned with solutions of the following quasilinear Schrödinger equations \begin{eqnarray*} -{\mathrm{div}}\left(φ^{2}(u) \nabla u\right)+φ(u) φ^{\prime}(u)|\nabla u|^{2}+…
Infinitely many solutions for a class of fractional Schrodinger equations coupled with neutral scalar field
Liejun Shen, Marco Squassina, Xiaoyu Zeng
We study the fractional Schrödinger equations coupled with a neutral scalar field $$ (-Δ)^s u+V(x)u=K(x)ϕu +g(x)|u|^{q-2}u, \quad x\in \mathbb{R}^3,\qquad (I-Δ)^t ϕ=K(x)u^2, \quad…
Normalized solutions for a fractional Schrödinger-Poisson system with critical growth
Xiaoming He, Yuxi Meng, Marco Squassina
In this paper, we study the fractional critical Schrödinger-Poisson system \[\begin{cases} (-Δ)^su +λϕu= αu+μ|u|^{q-2}u+|u|^{2^*_s-2}u,&~~ \mbox{in}~{\mathbb R}^3,\\ (-Δ)^tϕ=u^2,&~…
Multiplicity of normalized solutions for the fractional Schrödinger equation with potentials
Xue Zhang, Marco Squassina, Jianjun Zhang
We get multiplicity of normalized solutions for the fractional Schrödinger equation $$ (-Δ)^su+V(\varepsilon x)u=λu+h(\varepsilon x)f(u)\quad \mbox{in }, \qquad\int_{…
Planar Schrödinger-Poisson system with steep potential well: supercritical exponential case
Liejun Shen, Marco Squassina
We study a class of planar Schrödinger-Poisson systems where is a parameter, $V\in…
Normalized solutions to the Chern-Simons-Schrödinger system: the supercritical case
Liejun Shen, Marco Squassina
We are concerned with the existence of normalized solutions for a class of generalized Chern-Simons-Schrödinger type problems with supercritical exponential growth $$ -Δu +λu+A_0 u…
Concavity principles for nonautonomous elliptic equations and applications
Nouf Almousa, Claudia Bucur, Roberta Cornale +1
In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the…
Concave solutions to Finsler -Laplace type equations
Sunra Mosconi, Giuseppe Riey, Marco Squassina
We prove concavity properties for solutions to anisotropic quasi-linear equations, extending previous results known in the Euclidean case. We focus the attention on nonsmooth aniso…
Concavity properties for quasilinear equations and optimality remarks
Nouf M. Almousa, Jacopo Assettini, Marco Gallo +1
In this paper we study quasiconcavity properties of solutions of Dirichlet problems related to modified nonlinear Schrödinger equations of the type $$-{\rm div}\big(a(u) \nabla u\b…
Stein-Weiss type inequality on the upper half space and its applications
Xiang Li, Zifei Shen, Marco Squassina +1
In this paper, we establish some Stein-Weiss type inequalities with general kernels on the upper half space and study the existence of extremal functions for this inequality with t…
Local Uniqueness of blow-up solutions for critical Hartree equations in bounded domain
Marco Squassina, Minbo Yang, Shunneng Zhao
In this paper we are interested in the following critical Hartree equation \begin{equation*} \begin{cases} -Δu =\displaystyle{\Big(\int_Ω\frac{u^{2_μ^\ast} (ξ)}{|x-ξ|^μ}dξ\Big)u^{2…
Ground states of Schrödinger systems with Chern-Simons gauge fields
Yahui Jiang, Taiyong Chen, Jianjun Zhang +2
We are concerned with the study of existence of nontrivial ground states solutions for of Schrödinger systems with Chern-Simons gauge fields.
Uniqueness of the critical point for solutions to some -Laplace equations in the plane
William Borrelli, Sunra Mosconi, Marco Squassina
We prove that quasi-concave positive solutions to a class of quasi-linear elliptic equations driven by the -Laplacian in convex bounded domains of the plane have only one critic…
Concavity properties for solutions to -Laplace equations with concave nonlinearities
William Borrelli, Sunra Mosconi, Marco Squassina
We obtain new concavity results, up to a suitable transformation, for a class of quasi-linear equations in a convex domain involving the -Laplace operator and a general nonlinea…
Nonlocal approximations to anisotropic Sobolev norms
Ivan Cinelli, Gianluca Ferrari, Marco Squassina
We obtain some nonlocal characterizations for a class of variable exponent Sobolev spaces arising in nonlinear elasticity, in the theory of electrorheological fluids as well as in…
Critical gauged Schrödinger equations in R^2 with vanishing potentials
Liejun Shen, Marco Squassina, Minbo Yang
We study a class of gauged nonlinear Schrödinger equations in the plane. We obtain existence of two nontrivial solutions via the Mountain-Pass theorem and Ekeland's variational pri…
Nonlocal characterizations of variable exponent Sobolev spaces
Gianluca Ferrari, Marco Squassina
We obtain some nonlocal characterizations for a class of variable exponent Sobolev spaces arising in nonlinear elasticity theory and in the theory of electrorheological fluids. We…
An asymptotic expansion for the fractional -Laplacian and for gradient dependent nonlocal operators
Claudia Bucur, Marco Squassina
Mean value formulas are of great importance in the theory of partial differential equations: many very useful results are drawn, for instance, from the well known equivalence betwe…
Sobolev versus Hölder minimizers for the degenerate fractional -Laplacian
Antonio Iannizzotto, Sunra Mosconi, Marco Squassina
We consider a nonlinear pseudo-differential equation driven by the fractional -Laplacian with and (degenerate case), under Dirichlet type conditi…
Approximate convexity principles and applications to PDEs in convex domains
Claudia Bucur, Marco Squassina
We obtain approximate convexity principles for solutions to some classes of nonlinear elliptic partial differential equations in convex domains involving approximately concave nonl…
Modulational stability of ground states to nonlinear Kirchhoff equations
Jianjun Zhang, Zhisu Liu, Marco Squassina
We investigate the stability of ground states to a nonlinear focusing Schrödinger equation in presence of a Kirchhoff term. Through a spectral analysis of the linearized operator a…